Couple of suggestions:
* Hunter Hunted. It's an old Sierra side-scrolling platform game. You can play through a set of 1-player, 2-player co-op, or 2-player deathmatch missions. Plays at 640x480 resolution. Controls would be an 8-way and up to 6 buttons/player. (I recently put together a CD image of this with a new installer so I could try it out with an arcade controller, but alas I don't actually have mine built yet! If anyone else wants to try it out I am curious how it would play) Downside: Mouse or trackball of some sort would be required to navigate the menus.
* Lode Runner Online. Another Sierra game, this one despite having 'online' in the title supports two players on screen at once. It's a much amped up Lode Runner and is available as abandonware (from the programmer's site no less - search Google)