Bob Roberts has a tutorial on how to coin up games that don't have free play, and without hacking up your cabinet. But don't ask me to find the link. His site is in such a way that if you read something you better copy the URL.
Ok, well, I'm not going to give you a hard time for forgetting how to use Ctrl-F on Bob's website, but the method he describes only works for games that actually have start buttons. Basically, you just run one wire from the credit switch to the Player 2 start button, and then when you press that button, it adds a credit. Press it again to add a credit and start a 2 player game. Or, press the 1 player button for a one player game. It's clean and elegant, but nobody will figure it out, you have to tell them how to credit the game. Also, there are a few games that don't like this, since two inputs are getting shorted together. Plus, there's the timing involved, and if you hold the button down it might not credit.
(For the search-challenged,
http://www.therealbobroberts.net/freeplay.html)
Games like Simpsons don't have start buttons, so this really won't work. Also, the four coin slots on The Simpsons are separate, since they add credits for that player. So you really need four independent coin switches.
If you don't want to just use coins, you could do as mentioned above, mounting a switch behind the coin reject so that pressing it credits the player. I know it's not obvious to guests, but you could put a little instruction card on the machine. Of course, this assumes your guests can read. I have found that many cannot. Drilling holes in the cabinet is unacceptable, but sometimes you can get clever, replacing lockdown bar holes with pushbuttons, or replacing a control panel carriage bolt with a small button. Again, hard for guests to figure out.
Though, be honest, and think about it - even if you did the blatently obvious, and drilled four holes in the front of the cabinet, and mounted four color coded pushbuttons... would your guests figure it out? Probably not. That's not the standard method of coining up a game. You'd still have to tell them. So, I'd just mount switches behind the coin rejects and be done with it. Just, tell people how to use it. If you leave the mechs in the game, and people don't figure out how to credit it... maybe you'll make a couple bucks. Heh.
Personally, all my games are set to take quarters, and I have a jar of them in the arcade area.
-Ian