I'm killing time right now so I'll get you started with the rom names of 2 player versions of popular 4 player games:
simpsons2p The Simpsons (2 Players World, set 1)
gauntlet2p Gauntlet (2 Players, rev 6)
Teenage Mutant Ninja Turtles (Japan 2 Players) (there was no 2p version for USA or World as far as I can tell)
ssridersabd Sunset Riders (2 Players ver ABD)
As CrazyKongfan said, these variations, usually assigning characters based on coin-slot used, add a character select screen.
If you want, you can just enter the name of any 4-player game on
MAWS and they'll list the clones, usually including 2-player variations. If there's not one listed, you may be able to change the settings in the dip switch or service mode settings (to change a game from 4 to 2 player - I think NBA Jam and Revolution X are examples).