There are a bunch of games where inserting a coin also starts your game, like the Simpsons or Xmen games. You'd choose a coin slot that corresponds to a character and go from there.
If you wire up a coin button that inserts a coin for all 2/4 players, you'll instantly have 2/4 players on the screen.... even if its just you playing.
That said, most of these games came with versions where characters could be chosen, so you might be ok. I prefer having a coin button for each player though, but I put them off the control panel whenever possible.