I will check the ground. I did try new wiring, but with the same ground. All of the buttons are on the same ground. The coin for player one is the first one in the chain, so that could be it. I'll have to get a multimeter and check it out.
The reason I want a player one coin is two-fold. It's a cocktail table, so when I'm playing one-player, it's annoying to reach over and hit the coin button. Secondly, some games, like Guantlet, require each player to have their own coin button to get credit.