They don't have to be THAT big, it's just signal-level stuff, right? That's the saving grace. If there was any power involved, it would be have to be pretty big - but I've seen 1H coils the size of a marble. If you had a coil that was adjustable from 100mH to 1mH, and had a 100µF NPO cap... uh, that component might actually be bigger than the coil... anyway, you could tune the tank circuit from 50 to 500hz.
You need one with an adjustable core, though. The usual adjustable core units are for RF work and have uselessly small inductances. You may wind up having to make your own.