Yes, the pressure tank is the quietest option. You will have to have some way to pressurize it, however. That means you still need access to a compressor. If you have one already, you're set. Otherwise, plan to lug the tank back and forth to a service station.
High-pressure compressed gas cylinders are also quiet, but expensive and bulky. Available from a local distributor.
Small airbrush compressors from Paasche and Badger can be pretty quiet, though not completely silent by any means. Personally, I'd go with that option if all I wanted was to drive an airbrush. Hauling around a tank doesn't appeal.
My opinon only, of course. Let us know what you decide.
The air tank as mentioned is your first option and definitely will be quiet. If that doesn't work for you then the next option would be a compressor that has a "air on demand" type feature. I have a Badger Whirlwind 2 compressor and it only kicks on when the psi drops too far below your set psi. This works great for me and I can use my compressor in the spare room while Y and the little on sleeps in the other room.
If you're using a pump-it-up-yourself tank, then the inexpensive air-tool regulators sold at Home Depot and similar stores will work just fine. A water trap is a very good idea, too.
If you're thinking of the high-pressure compressed gas cylinders, then you need an appropriate regulator for the tank. Very pricey, and available from the same distributor that handles the cylinders, or from a scientific supply house like Fischer Scientific.
Can't speak to the inner tube trick. Sounds interesting, though.
Are there still the airesol can type air supplies for air brushes? Seems I recall years ago from my HO days that you could buy aresol type cans that delivered enough pressurized air for one project. Never tried it.
Also, if you own your own home, you might consider. plumbing in an airsupply from your garage to your quite place. 3/4 galvanized pipe works well for this. That way you can run your compressor in the garage, connect it to your internal pipes and add a regulator indoors.
But if you ask me, the first suggestion "Air tank" is the best. I have one myself, and use to use it for running my finish nailers off of in places I couldn't reach with a compressor. To fill it to 100 psi you need a compressor that will at least deliver 135 psi.
They still have the cans to hook to your airbrush, Pretty pricey though and they tend to ice up if you use them too long at a stretch. Airbrushing seldom takes too long anyway, more time is spent cleaning the darned things-which is why I seldom use mine. Jerry
One thing to consider is constant pressure. If you go with the tank or tube ideas as you start to run low the pressure can vary. I don't know what you are planning to use your airbrush for but I would hate to run out of air pressure in the middle of something. I have never used the aerosol cans myself but I have heard the same thing happens with them.
I'm of the same opinion as Jerry. I don't use mine unless its a really big project, or I have several things to air brush.
As far as running out of air, I run my brush usually a touch under 28 psi most of the time. You don't need a lot of pressure. I have a small 3 gallon air tank that I fill to 100 psi and it takes a while to empty. Usually it can be filled while I'm changing out paint or cleaning the tip.