I. The argument from disagreement:
1. People and cultures disagree extensively about what is right and wrong.
2. Probably, if moral judgments were objectively true or false, people would not disagree extensively about what is right or wrong.
3. Therefore, probably, moral judgments are subjective.
This is the flip side of the argument from moral agreement. I don't think theists or moral objectivists would find this a very persuasive argument. The objectivist can claim that there is a common " moral core" - as we saw in the argument from moral agreement. While I think the evolutionary view is better at explaining the existing variety of moral codes, the objectivist is free to interpret the same evidence differently.
(Michael Ruse thinks morality evolved, but is nontheless objective. His argument doesn't seem very coherent, though, as pointed out by Jason Rosenhouse.)
Another objection: the theist can argue that true morality only comes from an understanding or acceptance of his/her preferred god, and those who have different moral codes are simply wrong.
A more difficult challenge for the theist (specifically, the Christian) is to explain how moral codes change over time. Christianity accepted slavery as part of the divinely ordained order of things for more than 1000 years. Yet today most Christians would say that slavery is wrong. (William Lane Craig is one who bites the bullet and says that Biblical slavery was not morally wrong. He also defends Biblical genocide - which is why Dawkins refused to debate him. I'm not finding the link to his Reasonable Faith post about slavery (he calls it "indentured servitude"), tho.) So how is it that God-based morality was so much in error for so long? But theists have potential answers to this challenge, too. (For instance "continuing revelation" or an evolving understanding of God's will.)
Unfortunately for the subjectivists, this might be the strongest argument they have.