Another solution is to get an air tank and regulator without a compressor at all. You can buy a 15-gallon tank for about $15 at Sears. You only need to take it to a local gas station to refil it, or you can also get a loud air compressor of your own, fill it up in the parking lot (or wherever) and then use the silent tank inside.
I'm not sure how long such a tank would last, but I can say that I have an industrial compressor with a 15 gallon tank which I pump up to 100PSI and then turn off the motor. I can run the airbrush for 45 minutes (not continuously, but that much painting time) and use maybe 1/2 of the air.