When Martin Luther King was alive, he had a lot of detractors. Perhaps the most common claim made against him back in those days was that he was a communist. This was, of course, during the Cold War and so that was a pretty potent accusation. It was partly because of this that the FBI wiretapped and did other forms of surveillance on him.
Since his death, he has come under criticism from relatively mainstream sources for two other things:
1. Alleged plagiarism in some of his sermons and in the dissertation he wrote to earn his Ph.D.
2. Marital infidelity (captured on some of the FBI tapes of him).
As far as websites, there are a fair number of them out there, and I'll link you to some. But you should be aware that a lot of this stuff is overtly racist or is posted by groups with connections to neo-Nazi types (I know Stormfront (link 2 is a neo-Nazi group). I am NOT advocating the message of these groups NOR am I saying that their claims are true. However, you asked for anti-MLK websites, and these qualify.
You can follow this link for a "truth check" on some of the accusations made by the links I provided:
This link has some discussion of why some people opposed making MLK Day a holiday...
If this isn't what you need, post here, or message me.
He plagiarized in his work to get his Phd.
However, what do you mean by "against him"? Do you mean his character or what is most synonymous with his name, his leading of the protests?