This was a while ago from someone analyzing Tribunal cases: http://forums.na.leagueoflegends.com/board/showthread.php?t=2445574
First, we'll compare how often a champion is reported to how often it is played.
Tryndamere - 15.8% report rate
Twitch - 15.6%
Master Yi - 15.1%
Evelynn - 14.9%
Mordekaiser - 13.9%
...
Ahri - 6.8%
Sona - 6.0%
Taric - 5.9%
Leona - 5.6%
Janna - 5.4%
So when seen, Tryndamereis the the most likely to be reported, and Janna the least.
That covers reports, but once reported, who is most likely to be punished?
Irelia - 77.7% conviction rate
Udyr - 77.6%
Volibear - 75.9%
Trundle - 73.3%
Xerath - 73.2%
...
Maoki - 57.6%
Malphite - 56.8%
Skarner - 55.7%
Jayce - 54.2%
Leona - 52.6%
(NOTE: this was back in 2012.)
Here's something more recent from Reddit: http://www.reddit.com/r/leagueoflegends/comments/1ynzsg/champions_played_by_the_most_toxic_players_chart/
However, this is correlation and not necessarily causation. It's not clear if toxic players gravitated towards these champions, or that they were frustrating to play against and so people just reported them more out of spite/frustration. But given that the bottom of both lists is pretty much all supports, there's probably some factor of angry players preferring carries and not more team-oriented champions.