Suffice it to say that no argument for the existence of a transcendent deity has proven to be generally persuasive or has withstood rigorous philosophical analysis.
To the first part one must ask, "Generally persuasive to whom, by what measure; and how do other arguments fare on this metric?" And the next part is just false; several arguments for God's existence have stood up to rigorous philosophical analysis as well as any philosophical argument ever has. One thinks also of Weisheipl's discussions of Aquinas's First Way, or Gyula Klima's discussion of Anselm's argument. In fact, it's often child's play to show that alleged rigorous refutations of arguments for God's existence are confused and ill-informed. Madigan also completely conflates the claim that "morality comes from a divine source" with the much narrower and much less common claim that "morality consists entirely of divine commands" (divine command theory).
The second part is somewhat better. Madigan unfolds a "naturalistic alternative view" by looking at the discussions of James Rachels and Frans de Waal. I haven't read de Waal's book, but I found Rachels's book to be a massive disappointment; all the major philosophical work in the book is really done by a very crudely formulated problem of evil, and, although it is supposed to be about the moral implications of Darwin, the connection Rachels builds between the view he presents and real Darwinism, i.e., the basic evolutionary idea of the Origin of Species, is tenuous at best. Madigan quotes a typical example of Rachels's utter absurdities:
Before Darwin, our understanding of the nature of non-humans was controlled by a certain picture of the world: according to this picture, the gap between human nature and animal nature was established once and for all by God in his original act of creation. To men he gave souls, free will, rationality, and moral judgement, the other animals he created as lesser beings. Against the background of this picture, any attribution of moral qualities to animals would seem impossible. What is needed, in order to make such attributions possible, is the substitution of a different picture. Darwin provided the new picture, and tried to show that once it is adopted the view of animals as (at least partially) moral beings follows naturally.
But it is easy enough to show that Darwin didn't provide the picture at all, particularly where morality is concerned. The significance of Darwin was not that he gave a way to attribute moral qualities to animals. It was (need it actually be said?) that he gave a powerful argument for a gradualist account of the origin of species. Darwin's amateur reflections on morality can easily be shown to be derivative; from Hume, for instance, who makes a stronger case than Darwin does for attributing moral qualities to animals. It may be hard to imagine, but Darwin was not an all-shattering trumpet-blast opening the first round of Ragnarok. Almost always, when people open a sentence with "Before Darwin" you know that they are trying to pull a fast one; the only such sentence that is clearly true is, "Before Darwin we didn't have anyone pompously telling us how things were before Darwin." And, contrary to Madigan's claims, only someone very uninformed would hold that most religions assume that human beings begin with regard for every member of our species.
There is also the relatively uncritical identification of morality with altruism in the biological sense; an identification I have never understood, since it can easily be shown to result in conclusions that almost everyone would recognize as moral absurdities. The reason it was ever an issue at all, I imagine, is that some people considered it difficult to see how Darwin's theory could allow for disinterested regard at all, which morality would seem to require at least some of the time. In other words, the question was only whether a roughly Darwinian theory could provide the materials that morality presupposed. If it couldn't account for even a very basic sort of altruism, it was clearly false, and stood no chance of connecting up with a satisfactory account of morality. But if you have an account of how altruism arises, you do not yet have an account of morality; all you have is an account of a certain sort of behavior, not of its being moral. Why it should be singled out in the way morality does single out actions from other actions is still utterly mysterious. (Just judging from the quotations of him that are given by Madigan, de Waal seems to recognize that the issue of altruism only touches on the requisites of morality; but Madigan does not.) Madigan also confuses two things when he talks about "seeing oneself in the plight of another". A good case can be made that sympathy, in the Humean sense, is a basic building block of morality; but this does not prove anything about the relation between morality and sanctity or divinity. "Seeing oneself in the plight of another" is a plausible basic building block for morality, but "Recognizing that seeing oneself in the plight of another is a basic building block for morality" clearly is not; nor does it follow from the latter claim's being independent of anything that morality is independent of it. Unless, of course, Madigan is willing to concede the Cartesian argument for dualism; because that's precisely the way a Cartesian proceeds. Likewise, it does not follow from the fact that moral tendencies are independent of religion that they can receive adequate rational justification independent of religion -- the latter is clearly what is at stake in the question, and Madigan doesn't even touch on its outlying periphery.
I confess, I find the pompousness of naturalists on this subject rather funny. Madigan's ending is a good example:
There is still much that needs to be learned about the connections between human morality and other animal behavior. The scientific attitude is better able than dogmatically-based religions to pursue such an understanding, for it is not beholden to ancient writings or priestly authorities in its explanation of the moral sense.
Oooh, what a clever conclusion. On this subject you can always measure how lousy a naturalist's rational arguments are by how much they need to dial up the rhetoric in order to compensate.
Incidentally, just as a byway, if people like Madigan and Rachels are right that we should somehow take Darwin's amateur speculation about the origins of morality as closely linked to his more serious evolutionary work, utilitarians should all just throw in the towel. Darwin was a moral intuitionist; the morality he explains the origin of is not utilitarian, but intuitionist. (Intuitionists, of course, don't necessarily reject utilitarianism, although some do; they hold that it cannot be taken as an adequate account of the whole moral landscape.) Utilitarians don't actually need an evolutionary explanation of morality, any more than mathematicians need an evolutionary explanation of game theory; from a utilitarian perspective what evolution provides is simply the principles on the basis of which the interests of the agents are fixed -- the conditions of our particular game, as it were. All it needs is for evolutionary theory to stay out of its way, i.e., not introduce any barriers to its account. Certain kinds of intuitionist, however, and in particular, most modern naturalistic intuitionists, are utterly dependent on there being a viable evolutionary account of what they deem to be the fundamental moral intuitions -- sympathy or moral approval or what have you.