I'm redating this post.
I think there are two cases of atheistic morality that would have to be considered. Some world-views are not theistic per se but believe that there is a given purpose for human existence. If you accept something like Aristotle's inherent purposes (Aristotle had the unmoved mover but the UMM is not a personal God), then what is right fulfils that purpose and what is wrong fails to do so. I'm not sure that the idea of inherent purpose makes sense without the idea of intended purpose, but if you bought that it looks like you can get an objective moral standard out of it.
A theistic account of morality would, I think, combine the idea that as creatures of God we are created in such a way that our intended purposes and our inherent purposes are identical: we fulfill our purpose as human beings by doing what we were made to do. (How that solves particular problems like abortion, for example, may be more difficult, but right now I'm just working on the general idea of a moral life).
If you're going without God and without inherent purpose, then I think Hume is about the best source. He pointed out that a lot of ethical behavior can be justified by enlightened self-interest or social utility, and that we have feeling of sympathy for one another. But with his system, I have trouble seeing why we should do the right thing when it isn't in our enlightened self-interest and when we are feeling a lot of other feelings a lot more strongly than we feel sympathy. Why should sympathy trump other, stronger, feelings?