I used to buy Converse almost exclusively for my non-dressy shoes, until they moved their plants outside the U.S. to places like Indonesia. I'm almost positive the shoes made by Converse there use child labor, and I'd have to say it ranks higher on my "Do Not Buy Ever" list than leather.
I'll do some more research before you accept that as fact, though.
EDIT: I do know they were purchased by Nike, though, so that makes me 99.99% sure they use child labor. But let me find some proof.