Depends - is it stuck even when the game is turned off? Or, does it just energize and stay energized while the game is on (turn it off quickly if this is the case).
If it's stuck when the game is off, it's not just hung up, and you notice that it's difficult to manually move it back and forth, odds are good the coil will need to be replaced as you were told.
If it's only stuck when the game is turned, then the root cause is likely the respective driving transistor on the lamp/solenoid driver board, and that transistor needs to be replaced at the least. If the game was left on for any length of time (IE longer than a few minutes tops), odds are good you'll want to replace the coil as well.
If you have no clue what I'm talking about, at the least you'll need to send your driver board out for repair, and may well need to have somebody replace the coil for you as well. No need in either case to buy a completely new board really.
Manual:
http://mirror2.ipdb.org/files/125/Bally_1982_Baby_Pac_Man_Manual.pdf
I show the right saucer as driven by transistor Q38 - test it, and replace it as necessary. Check the associated diode and resistor near it while you're at it.
The coil is an AO-27-1300 - you should have no problems finding a replacement. Use a TIP-102 for replacing the transistor.
Good luck!