There are several devices out there that will make the 10/22 fire rapidly in a legal manner. The best of these (I've tried 4 different ones) is the GAT trigger crank system. This is a well-made assembly that uses a cam-type crank combined with a trigger bar that contacts the bottom of the trigger. As you turn the crank, the bar moves in and out firing the gun four times per turn of the crank. Check it out at:
You can find them at http://www.gunbroker.com
if you do a search under GAT. The going rate is $27 delivered. Don't get the BMF activator or any of the hellfire, hellstorm, etc. types of 'inertia' trigger devices. These are finicky and difficult to get working properly.
The GAT is an excellent way to satisfy your need to burn up a brick of ammunition in about twenty minutes. Good luck.