I love this community, got so many recomendations I decided to update the first post! Sorry if I couldn't reply to everyone, Jerboa almost exploded, haha. But I'll upvote all your contributions now that I'm on PC.
Original post
I like to play on the same computer with my bf, and recently we've started to get tired of MAME since we've been playing our faves on repeat for so long.
The other game we play is Spelunky, since is the only local co-op game I have on Steam. I ask because Steam summer sales are close and I can give him a surprise :D
I was a bit confused when you said local co-op. It implies 2 computers on the same local network(connected to the same router, no internet connection required). I think the term you're looking for is split screen gaming.
When I looked at pictures of Spelunky games like Clonk and Liero popped into mind, I think there are options for split screen multiplayer in those games, they're old school PvP games.