Is this Gottlieb Pinball Pool?
The part number should be in the manual. If he does not have the manual, he will need to purchase the manual.
I suspect Steve Young at Pinball Resource can tell you what coil you need, without the manual.
http://www.ipdb.org/faq.html#faq17
But your bigger problem is solving what caused the coil to burn up. And check to insure that the correct fuses are installed in the game. Usually when a coil burns out like that, it is locked on - shorted out. That can be caused by a bad transistor on the driver board. That will require board repair. There is some troubleshooting that will need to be done to narrow it down.