Thanks JFB.
vRJs reply is succinct and to the point, there is no silencer
made for the P3AT.
The biggest problem is the threaded barrel because of the thin wall and the pinch in the muzzle. This alone is pretty much a show stopper, there's no way to thread that pinch, someone would have to mill a whole new barrel long enough and thick enough to thread.
The next biggest hurdle is the suppressor itself. The .380 is, for all practical suppression purposes, a 9mm and while there are many 9mm suppressor choices out there the majority add too much weight to the muzzle for the P3AT to cycle properly. There are two micro cans that might be usable, the Thompson Poseidon and the DeGroat Nano.
DeGroat Tactical has successfully threaded a Sig P238, it has thicker barrel walls and no pinch in the muzzle. You can see the seam where the adapter is threaded on the barrel.
http://armamentsales.sslpowered.com/photos/displayimage.php?album=36&pos=41
The Kahr 380 might be adaptable, I'm looking into that now but it's not promising since the barrel wall is thin on that gun as well.