It's tough to find many as a lot are defunct now, but I did a search and this one appears to be still running: trope_bingo. Most bingo cards will focus on a fandom or pairing but like this one, can focus on something like tropes, hurt/comfort, etc. Each card may have different rules, but basically you accept a card given to you by the Mod and there is usually a deadline, but that's not set in stone.

You may be able to ask for any leads at http://avengerkink.livejournal.com for Marvel-based cards, and maybe at http://norsekink.livejournal.com.

I would also search under the tags 'bingo' and 'bingo card' at AO3, because there are active cards there.

Hope that helps! :)