The people who make this argument are claiming, in effect, that God is by definition an uncaused cause, but we can properly ask “What caused God?” with exactly the same tenacity that theists ask “What caused matter?” And why is God exempt from having a cause, but matter or physical laws are not? This is just sophistry. Faitheist philosophers are always telling us that we don’t grasp the subtleties of theological argument, but that won’t wash here: Manzi’s argument is identical to that made by Aquinas and refuted by Hume and his successors. It ain’t subtle. You can look up the details.
I hope people do, because Hume's argument is rather more sophisticated, and rather more limited, than Coyne suggests.
It's worth actually considering the part of Hume's text in which this argument comes up, namely, the Dialogues Concerning Natural Religion, Part IV. Contrary to what Coyne implies, of course, Hume doesn't have Aquinas in view. He probably never actually read Aquinas. Coleridge claimed at one point to have found a copy of Aquinas's commentary De Memoria; that would be great if true, since it would give a nice explanation for why Hume's principles of associationg are so similar to scholastic accounts of reminiscentia, but Coleridge was almost certainly wrong. So we have no reason to think that Hume had even read any Aquinas. Nor is he getting an Aquinas-like argument from some other source, because the argument he has in view is very, very specific.
The Dialogues is a conversation between three people: Cleanthes, Demea, and Philo. Cleanthes is a Newtonian theist along the lines of Colin Maclaurin. Demea is harder to pin down, although he appears partly influenced by Samuel Clarke; but he's not really relevant to our particular argument, so we can set him aside for the moment. And Philo, who is good friends with Cleanthes, is a skeptic. In some ways he's a stand-in for Hume, but there are several points in the dialogue where Hume lets Philo go too far in order to be fought back by Cleanthes; Hume is not interested in treating Cleanthes as a caricature, and he does an excellent job of keeping up the dramatic interaction. Cleanthes wins a few points, and also is the one who gives Hume's reasons for rejecting Demea's a priori argument.
Cleanthes had put forward a design argument based on the principle that like effects have like causes. (This is a very Humean principle to use; Hume lists it among his causal maxims in Treatise 1.3.15.) Cleanthes insists that the design argument is the only possible source of information about God, and at the beginning of Part IV actually goes so far as to call traditional theists Atheists, because they don't strictly follow the principle of like effects having like causes. Turnabout being fair play, Demea calls him an Anthropomorphite. As Philo notes, it's a little odd to call all idolaters and Christian theologians Atheists, but he begins to argue with Cleanthes on his own terms, with the specific intent to show that there are "inconveniences" in Cleanthes's Anthropomorphism, and in particular to argue that, whatever else it may be, there are problems with thinking of the world being caused by a diversity of distinct ideas arranged in a particular order like the blueprint of an architect. Thus he says:
It is not easy, I own, to see what is gained by this supposition, whether we judge of the matter by Reason or by Experience. We are still obliged to mount higher, in order to find the cause of this cause, which you had assigned as satisfactory and conclusive.
If Reason (I mean abstract reason, derived from enquiries a priori) be not alike mute with regard to all questions concerning cause and effect, this sentence at least it will venture to pronounce, That a mental world, or universe of ideas, requires a cause as much, as does a material world, or universe of objects; and, if similar in its arrangement, must require a similar cause. For what is there in this subject, which should occasion a different conclusion or inference? In an abstract view, they are entirely alike; and no difficulty attends the one supposition, which is not common to both of them.
So the problem is that, if the plan in the divine mind simply mirrors the universe itself, as Cleanthes's Anthropomorphism requires, we are faced with the problem of now having twice as much to explain: a material world and its exact immaterial duplicate. Since the ideas exactly duplicates the world, or, rather, the material world exactly duplicates the ideal world, everything that holds of one holds of the other, so Cleanthes's Anthropomorphism commits him to turning God into just an ideal world and saying that the cause of the material world is that ideal world. But then, says Philo, we have turtles:
Have we not the same reason to trace that ideal world into another ideal world, or new intelligent principle? But if we stop, and go no further; why go so far? why not stop at the material world? How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression? Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world. By supposing it to contain the principle of its order within itself, we really assert it to be God; and the sooner we arrive at that Divine Being, so much the better. When you go one step beyond the mundane system, you only excite an inquisitive humour which it is impossible ever to satisfy.
So in other words, since Philo has argued that Cleanthes has effectively turned God into an ideal world that exactly duplicates the material world, it would be much more parsimonious simply to get rid of duplicate worlds altogether and make the material world God. (Philo will come back to this suggestion more than once.)
Cleanthes is unimpressed by the argument: "Even in common life, if I assign a cause for any event, is it any objection, Philo, that I cannot assign the cause of that cause, and answer every new question which may incessantly be started?" That is, if you have an argument that Y causes Z, it is unreasonable to deny that conclusion simply on the basis that you haven't shown what causes Y. That would be to guarantee that no causal explanations could ever get off the ground. The "common life" point, by the way, is a sharp crack at Philo: Philo has already put a great deal of emphasis on common life, a phrase that shows up repeatedly throughout the dialogue as central to Philo's view that we should not reason beyond what we find in common life. What is more, Cleanthes points out, everyone will eventually reach a point beyond which they can't give causes.
Philo concedes the point but says there is still a problem:
Naturalists indeed very justly explain particular effects by more general causes, though these general causes themselves should remain in the end totally inexplicable; but they never surely thought it satisfactory to explain a particular effect by a particular cause, which was no more to be accounted for than the effect itself. An ideal system, arranged of itself, without a precedent design, is not a whit more explicable than a material one, which attains its order in a like manner; nor is there any more difficulty in the latter supposition than in the former.
Philo doesn't give Cleanthes a chance to respond, but continues on to argue the inconveniences of Cleanthes's Anthropomorphism.
Let's stop here a moment and consider what's going on. Philo is not employing this argument against the basic position that the world has a cause. He is employing it against Cleanthes's contention that, contrary to the usual theistic position, the cause has to be as similar as possible to the case of an architect building a house on the basis of specific ideas ordered in a certain way. This, says Philo, effectively makes God an ideal world that the material world copies, and nothing more.
The difference is important. If it were a just a matter of the causal principle, giving a cause to the material world would be a matter of subsumption under a general causal law; but Cleanthes is proposing to explain the material world by an immaterial world that is completely isomorphic to it, and suggesting that, despite the fact that they are isomorphic, one arranges itself on its own and the other does not. But if the ideal world arranges itself on its own, then, given the isomorphism, so can the material world.
It's a very clever argument. The only possible option open to Cleanthes would be to argue that there is something special about ideas themselves -- that the very fact that the world is ideal is the one difference that makes a difference here. That's the way a Platonist would argue. But Cleanthes is not a Platonist, and this option is not open to Cleanthes: because he's committed himself a strict application of the principle that like effects have like causes, the ideas in question have to be like human ideas, but bigger. And human ideas, at least if you're not a rationalist, don't arrange themselves without "precedent design". Very clever. It's the first point on which Philo has blocked Cleanthes in.
It is important, however, to understand how limited it is. The Dialogues don't end here for the obvious reason that Philo hasn't refuted anything. All he has shown is that Cleanthes is committed to the existence of infinite duplicate worlds, each one cause of the next. But Cleanthes is right that the original argument still stands. Which raises the second point at which this is a very limited result: it all hinges not on the original causal argument but on Cleanthes's insistence that the cause has to be as exactly like a human mind, with its ideas, as possible. Cleanthes points out at the end of Part IV that all of Philo's "inconveniences" (of which he lists several more) do nothing whatsoever to eliminate the original argument. And Hume's Cleanthes is an honest and astute man: he is exactly right on this point.
It's not until Part VII that Philo goes beyond this to an idea that, he tells Cleanthes, "if just, must go near to subvert all your reasoning, and destroy even your first inferences." This is the famous series of different analogies, which leads into the Epicurean hypothesis in Part VIII.
In Part IX we find a character suggesting that if God might be necessary, we could just as well call matter necessary. It is not Philo, but Cleanthes. Demea has proposed that God is necessary in the sense that it would be contradictory for him not to exist. Cleanthes, still arguing that the design argument and only the design argument can give knowledge of God, will have none of it: he will accept no other argument, and so says,
But further, why may not the material universe be the necessarily existent being, according to this pretended explication of necessity? We dare not affirm that we know all the qualities of matter; and for aught we can determine, it may contain some qualities, which, were they known, would make its non- existence appear as great a contradiction as that twice two is five.
But the argument here is already based on Cleanthes's insistence that nothing exists necessarily; it's not a suggestion that the world exists necessarily but another example purporting how absurd it is to say that anything exists necessarily. Philo, however, uses the opportunity to deliver a subtle jab at Cleanthes by noting that adding necessity to the mix is dangerous because the numbers have an order that a "superficial observer" might think was due to chance or design, but that someone with sufficient insight could show was not designed at all, but necessary, and that one could by analogy reason that the world was like that, too. It's a subtle hint at another analogy that Cleanthes failed to consider. But, of course, Cleanthes would not accept that actually existing things ever have the relevant sort of necessity.
So Hume doesn't provide a refutation of Cleanthes's causal argument. Indeed, as commentators on the Dialogues have noted for quite some decades now, Hume's Philo explicitly denies having refuted it, and denies even trying to refute it. The closest he comes is in his comment that the analogies come "near" to destroying Cleanthes's original reasoning. But near is all: on a Humean account of analogy, analogies can't refute analogies. What they ultimately do is call into question Cleanthes's Anthropomorphism: not only must the original cause be like a system of ideas in the mind of an architect, it must also be like the cause of vegetation, animal generation, putrefaction, &c., and in some ways even more so. Like effects have like causes.
It is, of course, the case that someone can ask "Who made God?" as much as they can ask "Who made the material world?" But that's a feature of language, not of the subject matter. Anyone can ask any question about anything; the quesion is whether it makes sense to ask it given the arguments that have gone before. Philo points out that Cleanthes's argument, given the way he has taken it, makes sense of such a question. But this is not a refutation of the argument; it just clarifies what one is committed to. And Philo notes that if you decide to stop at matter instead, this is as much to say, Spinoza-like, that the material world is God, Natura naturans. Philo is able to press this issue not because of the causal argument itself, but as an "inconvenience" of Cleanthes's particular way of taking it. You will search in vain for a refutation of the causal argument itself; Hume very deliberately avoids giving one, very explicitly denies giving one. Commentators disagree as to why he does this.
As to whether others went farther, I don't know; I don't know who Coyne means by the "successors" of Hume. Russell, of course, raised it in the debate with Copleston; but he raised it as a challenge to be answered, not as a refutation in its own right. So, again, very limited. I'm not sure who else he would have in mind.
In the end, I think this sort of thing is why Coyne's approach is very likely to fail. It's not that he doesn't know the opposing arguments, e.g., those of Aquinas (who gives, explicitly, several arguments in the Summa Contra Gentiles why there has to be a cause of which it is incoherent to ask what caused it). It's not an ideal rational state, by any means, but as a straightforward matter of human history, lots of approaches have done very, very well despite ignorance of the arguments they opposed. But not knowing your own arguments is another thing entirely. It isn't really like demanding that Coyne have an intimate familiarity with the ins and outs of Iamblichus-style pagan Neoplatonism; it's simply the reasonable expectation that if Coyne is actually going to appeal to Hume as successfully refuting an argument that he would actually bother to take the trouble to do justice to that argument. And yet Hume's very subtle, beautifully designed argument gets mangled in the service of Coyne's sneering. People who don't respect their own arguments will eventually find themselves abandoned by them; having mangled even friendly reasoning, they will inevitably begin to look unreasonable altogether.