thats odd ... usually there are clips on the back of the coin door that hold it onto the coin door instead of carriage bolts 
Depends on the type of door. On over/under doors, there are the 'clip' things. On Midway and Williams style doors, they're mounted with carriage bolts.
Shmokes: trace a pattern on the front where the door is supposed to go (DON'T TRACE THE DOOR! Just the inside where it will insert into the cab) and cut that piece out. Then, place the door into the cabinet. With a pencil, mark where the holes in the door are. Remove the door, and drill out your holes. I think you want a 1/4" bit?
The square of the bolt will line up with the door, and the bolt will get secured from the inside. Note: use washers on the inside, along with your bolts.