Le grand argument, qui détermine notre Auteur à rejetter la pensée de ceux qui trouvent dans les rélations nécessaires des choses, les fondemens de la distinction de Juste & de l'Injuste, c'est non seulement, qu'il ne peut jamais résulter de-là des obligations proprement dites, mais seulement de simples motifs de convenance, pour déterminer à agir d'une façon plutôt que d'une autre;....
They translate this as:
The great argument that determines our author to reject the view of those who find in the necessary relations of things the foundation of the distinction between right and wrong, is not only that obligations, properly speaking, can never result from these relations, but only motives of agreement for determining one course of action rather than another.....
As you can see, they translate motifs de convenance as "motives of agreement." According to the footnote, a reviewer suggested that it should be translated "grounds of convenience," a suggestion which they firmly reject, and certainly rightly, since it's anachronistic. Appealing to the 1762 Dictionnaire de l'Académie, they note two contemporary definitions of the phrase, raisons de convenance:
(1) des raisons de pure bienséance
(2) des raisons qui sont probables & plausible, & qui ne sont point démonstratives
Their translation for the first "reasons of propriety" and of the the second "reasons that are probable and plausible, but are not demonstrative ones," and suggest that the second definition capture the probable meaning of the phrase here. I'm not entirely clear how their very, very literal "motives of agreement" is supposed to meet up with that definition. But, in any case, I think it's pretty clear that the probable meaning is not the second but the first, which should be translated not as "reasons of propriety" but "reasons of (pure) congruity" or even, if you are willing to allow the expansion, "reasons having a regard to appropriateness alone." Convenance throughout the early modern period is a quasi-technical term drawn from the scholastic Latin convenientia, 'appropriateness' or 'fittingness' or 'congruity'. An argument ex convenientia is an argument that's not demonstrative but based on an appeal to what's fitting. For instance, you can't demonstrate that God became man, but you can give reasons for thinking it fitting or appropriate or congruent. This is the root of both of the definitions given by the Dictionnaire de l'Académie.
The gist of the above passage, then, is:
The major argument of the author against the necessary relations view
is not merely that obligations cannot result from these relations
since they can only provide motifs de convenance for preferring one course of action to another
but....[and then he goes on to give the main line of the 'grand argument']
The complaint presented in this clause is presented as if it were a common one; the reviewer is saying that Hume does not merely present the common objection, but goes further. And the common objection that is presented here, I take it, is that necessary relations don't give you obligations, they just give you reasons for thinking it more appropriate to choose this rather than that. This is indeed a common objection against the necessary relations view in the early modern period; it's arguably the most common one. When Cockburn defends Clarke's position, to give just one example, it's this objection that looms largest and requires most of her ingenuity to rebut.
So, contrary to Norton and Perinetti, it is almost certainly the first of the two definitions they give that fits most closely with the reviewer's argument. I would translate the passage as follows, if I were allowing myself to be a little more dynamic than strictly literal:
The major argument, the one that leads our author to reject the idea of those who find the foundations of the distinction between right and wrong in the necessary relations of things, is not just that these can never result in obligations, properly speaking, only in arguments of appropriateness for resolving on one course of action rather than another;....
And so on. If I were doing it more literally, I would basically translate it as Norton and Perinetti have done, but the last clause would be "but only fitting reasons for resolving on one course of action rather than another."2
1 "The Bibliothèque raisonnée Review of Volume 3 of the Treatise: Authorship, Text, and Translation," Hume Studies 32.1 (April 2006) 3-52.
2 The astute reader will notice that I have translated the second determiner as "resolving on", i.e., developing a resolution in favor of. This is certainly one meaning of the term in this period, and fits the context well; it's also a little less obscure to say 'resolving on one course of action rather than another' instead of 'determining one course of action rather than another.'
Cross-posted at Houyhnhnm Land.