Frame Quirrell. (Assuming it's even framing and not accidentally getting the right answer for the wrong reasons.)
Harry knows he's an unregistered animagus. Harry has even better blackmail with Azkaban though he'd be loath to use it. People in universe also know that the defense professor is suspect #1.
Harry could just lie under veritaserum that Quirrell did all this. Nobody aside from Quirrell or Dumbledore would even imagine that Harry could do that (well, Snape and McGonagall). Way back in chapter 47, Harry said Bester thought Harry could beat veritaserum. Dumbledore and his faction would be unlikely to volunteer this information; Quirrell would have to GTFO of the country because he's an unregistered animagus (and also Voldemort, though Harry doesn't know that). Quirrell couldn't offer any legal challenge to Harry, so Harry could successfully pull it off against him.
Harry is certainly CAPABLE of framing Quirrel, but I don't think he's anywhere NEAR close to framing anyone he considers a friend. I think he's more likely to frame himself.
EDIT: New discussion thread here.
This is a new thread to discuss Eliezer Yudkowsky's Harry Potter and the Methods of Rationality and anything related to it. With two chapters recently the previous thread has very quickly reached 500 comments. The latest chapter as of 17th March 2012 is Ch. 79.
There is now a site dedicated to the story at hpmor.com, which is now the place to go to find the authors notes and all sorts of other goodies. AdeleneDawner has kept an archive of Author's Notes. (This goes up to the notes for chapter 76, and is now not updating. The authors notes from chapter 77 onwards are on hpmor.com.)
The first 5 discussion threads are on the main page under the harry_potter tag. Threads 6 and on (including this one) are in the discussion section using its separate tag system. Also: one, two, three, four, five, six, seven, eight, nine, ten.
As a reminder, it's often useful to start your comment by indicating which chapter you are commenting on.
Spoiler Warning: this thread is full of spoilers. With few exceptions, spoilers for MOR and canon are fair game to post, without warning or rot13. More specifically: