Yes that should work fine,
Cool. I was hoping I had at least some idea of what I was doing. LOL.
the coil only draws 12ma according to the data sheet, so you really don't even need the transistor on the output of the Arduino. Arduino output pins can withstand 40ma.
Trying to be safety boy.

All the stuff I read had me switching things like this with a transistor to get the full voltage of the circuit on relay coil.
Don't forget to put a diode on the solenoid as well.
Thanks for that. Noted.
You could simplify the system by using a single 12V wall-wart, 12V solenoid, powering everything off the same supply, and using your TIP120 to drive the air cannon instead of the relay
Well I had been looking at a solenoid like this one:
http://cgi.ebay.com/1-2-Electric-Solenoid-Valve-24-V-DC-Air-Fuel-B21N-/290538398689?pt=LH_DefaultDomain_0&hash=item43a57023e1I hadn't see a 12v one, but I will have to look now. I've never worked with them before and don't really know. I was trying to match up with what I see in the Air Cannons for Dummies video on YouTube.
The idea was to make that cannon driven by the motion sensor/Arduino.