The solenoid wouldn't even actuate with 12VDC. Of course since I sent everything to 1UP, I now have a Mad Planets (Gottlieb) cabinet that has a +30VDC source that Gottlieb uses for the sound board amp & knocker on Q*Bert. The Gottlieb power supply rectifies the +30VDC from a 35VAC tap off the transformer, so you would need both a Gottlieb transformer and power supply to get the +30VDC to power the solenoid.
Here's a pic of the power supply (upper right board):

...and the 20lb monster transformer:

A Williams power supply has a +27VDC source that may work (and easier to find than Gottlieb arcade power supplies), but again the +27VDC is rectified from a 20VAC tap from the transformer.
It may be just easier to find a pinball power supply & transformer to drive the coil?? I don't know the lowest voltage that will actuate the coil, but it definitely wouldn't work off of 12VDC.
##EDIT##
Just to clarify, what I tried was a real Gottlieb knocker powered by a lower voltage. Here's a pic of the Q*Bert knocker:

The lower voltage solenoids I tried didn't have much "knock" to them at all. I would say more like a mild tap.

I would imagine if you went through the trouble to wire up a knocker and ended up with a pitiful little tap, you would be quite disappointed with the results. I would say that powering a real knocker will get you what you really want, rather than taking the easy way and actuating a smaller solenoid.