Virtually anything that will slow down and/or contain the expanding gases will work. However, "silencer" is a bit misleading. All the screw-on thingy you have at the muzzle do, is to suppress sound the gases expanding at supersonic speeds give off, and almost eliminate muzzle flash.
There are probably hundreds of ways of producing a suppressor. The most durable is baffles, though. A simple, yet effective way is steel whool. The downside is that it burns up relativly fast.
Suppressing a .22lr is almost easier done than said. It's a small round that doesn't give off much heat. In other words, the expansion rate is smaller, hence, you don't need a big, bulky and expensive suppressor.
Virtually any rifle smith can make one. However, don't do anything illegal and try to make one yourself. Just to point it out, why suppressors should be so hard to get in the US is a mystery to me. Here we used to have a ban in the past, until the police realised that criminals who had illegal weapons really didn't bother with suppressors - and, whatever illegal business you can do with a suppressed weapons, you can do with an unsuppressed weapon. My point of view is that a suppressor for regular gun owners saves the neighbours for a potential headache and should therefor be legal as long as you're allowed to own a firearm.
Integrated suppressors are weapons with suppressors running the entire length of the barrel. These weapons are designed to be as quiet as possible - without adding a 30cm suppressor to the total length. Think of it as a ship with a double hull. The inner hull is obviously the barrel. In between there's a pocket of air, and finally, the outer hull. The difference from a ship, though, is that the barrel doesn't run the full length of the suppressor (~outer hull). Instead it ends, say a third from the muzzle. This is obviously to let the expanding gases have somewhere to go...
Here in Norway there are several smiths that make custom .22s with integrated suppressors. The best one is a BRNO bolt action. All you hear is the supersonic crack and the shooter giggling over his new "toy". For hunting birds and small prey, there's nothing better.