I tried a 5 gal air tank and a small, tire inflator compressor. The tank would only last 15 +/- minutes. But, that's not the worst part. It always ran out at the worst possible time. The little tire inflators are noisy, really noisy.... And, you still need a regulator and moisture trap.
If you are on a budget, try it. If you can spare the $$$'s, here's what I recommend.
Buy a compressor that has a reservoir tank. That way the compressor doesn’t run all the time --- much more family friendly….. I got a 2 hp model with a 6 gal. tank. The compressor will run once or twice during a 2-3 hour painting session. I installed a brass shut-off valve between the regulator and the compressor too. Air was bleeding through the air brush when it wasn’t being used. This caused the compression to run more than it should. Home Depot, Loews, Sears have several models in the $200 range. They come with a regulator and moisture trap. They are small enough to at least be luggable (fairly easily moved).
Watch for sales.
Jim