There is no such thing as an airgun suppressor as far as U.S. law is concerned.
If it will suppress an airgun (and isn't integral to the airgun in a manner that prevents its removal and use on a firearm) then it will also suppress a firearm (even if only for one shot) and therefore is a silencer in the legal sense and all NFA regulations apply.
If you want a detachable suppressor for an airgun, then you find one that will work for your airgun and go through the NFA process to acquire it.
If you want a suppressed airgun without the NFA hassle, you will need to purchase an airgun that is integrally suppressed from the manufacturer.
Airgun suppressors are worthless.
There are 3 components to the discharge noise of an airgun.
1. Sonic "boom" if the pellet exceeds the speed of sound. This is rarely an issue because best accuracy is typically not achieved with supersonic pellets.
2. Mechanical noise--hammer falling, springs/pistons moving/vibrating, etc.
3. Muzzle blast.
Obviously a silencer has no effect on components 1 or 2, however the last item is significant.
While the muzzle blast of an airgun isn't as energetic as that of a firearm, the more powerful PCP airguns exhaust a sufficient amount of high-pressure air from the muzzle to require hearing protection. Even conventional airguns can have enough muzzle blast to be objectionable.
A powerful spring-piston airgun's discharge noise is reduced by perhaps 30% by the addition of a suppressor. It provides some benefit, but it's typically not a pronounced sound reduction.
A powerful PCP airgun's discharge noise is virtually eliminated with subsonic pellets when a quality suppressor is added. All you hear is the valve being actuated by the hammer.