Warpman is actually not that bad once you get into it.
It has a two player mode, where you play together.
Several people ask for "Battle City" which is another Namco small box game that also has a two player mode.
I wanted to play Super Chinese once with a friend but we didn't get around to it. Also two player, co-op (the video shows 1 player).
I don't know if these games have continues though. I don't like games without continues. I am also not too fond of games with this "Atari" graphics, but I know many people like them. Especially if they had famicom multi-carts (pirate carts) , where you often found these games.
A friend of mine made a video of Pac-Land. I can't stand playing games with such bad graphics, but some players like them. Pac-Land is a platforming game where you move right to level 4 or so, then you get an item that makes you jump, you return back to the first level to give back this jump item, then you move right again. Well I don't remember exactly.