I bought this compressor off craigslist and was wondering if it's good enough to paint

Probably OK to do one or two panels at a time with an LVLP gun... not enough to do a whole car at one time...it's going to run alot and get hot, when this happens it creates alot of water in the air line, make sure you have a water filter at the gun and change it often...drain the tank frequently

Check the cfm of the compressor and compare it to the spray gun you're using. If your spray gun requires more cfm than the compressor can provide, you'll be in trouble when trying to paint an entire car.

Diaphragm machines are typically weak. I have used them for small panels in a pinch. Heat may also be an issue which means issues if you can't cool the air low enough for your filter(s).

You need a piston pump with min CFM of the gun you will use.

I now roll with a 7.5 HP, 2 stage on a 80 gal tank.

Ditto, 7.5 h.p., 2 stage, 80 gallon. Drive most any air tool or even a couple at a time. You don't worry about running "out" of air (read that as CFM).