Here are my posts on that topic, gathered together in one convenient location. I've got until Thursday to merge them together and condense the result into a 2000 word essay...
1) Introduction to the amoralist's challenge, and working with a conception of morality which allows us to make sense of it.
2) Self-interested reasons: Collective Rationality - answers why we, collectively, should be moral. But what if the question is asked at the individual level?
3) Self-interested reasons: The Good Life. Forces a (partial) retreat from egoism, but insufficient to justify full-blown morality.
4) Seeking neutral ground: the framework view, and rational non-cognitivism.
5) The analogy with prudence (rules out prudence as the standard of rationality; leaves open rational altruism and present-aim theories).
7) Agent-neutral reasons. (Rules out objective present-aim theories. Leaves open rational altruism and relativism.)
8) Motives and Reasons (some pressure towards relativism).
9) The adoption of ultimate ends (resisting relativism) [forthcoming, though cf. here and here].