I have never been much of a fan of the argument from morality for the existence of God. But I now think it's worth distinguishing that argument into two variants: the metaphysical and the epistemological. The metaphysical says that the existence of moral truths is best explained by positing the existence of God. That one I haven't been much of a fan of, though I haven't thought much about it, and quite possibly, were I to think about it more, I'd see more to it than that.
But the epistemological argument seems to me to be quite promising. It says that we do know moral truths, but the best explanations of how we know moral truths presuppose the existence of God. After all, it is really hard to give a non-theistic account of how our beliefs about rightness are responsive to the facts about rightness.
One might think the problem only afflicts certain ethical theories. Thus, it seems that the constructivist or maybe even that elusive beast, the non-theistic natural lawyer, has some hope for an answer. But I think not. For while constructivism could explain how our beliefs about normative and applied ethics (say, that it's right to act generalizably, or that one ought not break promises) claims are responsive to the truth, I doubt that it could explain how the belief that, say, constructivism is the correct account of rightness is responsive to the truth. (The claim cannot simply be a claim about how we use the word "rightness", say that the constructivist account of rightness has the best fit with our use of the word. For then if our use were to shift, the constructivist would be in trouble.)
The issue is simply this: only three plausible metaphysical views make moral goodness as such (as opposed to beliefs about goodness) be explanatorily efficacious, and hence allow for our beliefs to be responsive to the moral facts: optimalism (everything that exists is for the best), theism (possibly widely enough understood to include some varieties of deism) and Aristotelianism. The last of these raises explanatory problems (e.g., about transitions between species) that only theism and possibly optimalism can solve. And optimalism is implausible, since it is not plausible that there is a best world.