Modern day good "garage" compressors are pretty much noiseless. Noise is similar to noice of refrigerator, which is not much, is it? Of course, size is still an issue.
Incidentally, I've made a compressor from old
refrigerator's pump (I've found it in a dump) and a tank from a piece of thick pipe:
I had to add a number of bits and pieces I had already in my basement (or expropriated/redistributed from those, who didn't really need them (i.e. were looking the other way when I was around.)) As you see, there is no problem for us apartment dwellers with such compressor. As a matter of fact, it works so quiet, sometimes I forget to turn it off! Air goes through my airbrush with much more noice than compressor makes. Good thing I was able to expropriate appropriate circuit breaker, which turns off the compressor when pressure in tank is good.
Mind you, I'm not sure if my pressure regulator is precise. While everyone insist that working pressure for airbrush is 15-30 psi (I can get up to 60psi), my airbrush sprays acrilics jolly good on 4-5 psi, and problems starts when I up the pressure to 10. What the world have came to, you can't even redistribute reliable hardware anymore! :)