Are there any shotgun silencers available? Yes.

Are they available to you? No.

What first comes to mind when people are asking for a quiet way to "hunt" deer is that they're actually looking for a way to poach without anyone hearing them. I'm not saying that's the case, but if you're in the right with what you're doing, why do you need to hide it?

Suppressors of any sort are considered Class III, prohibited in many states completely, and requiring a background check and annual $250 excise tax just to be able to own one...A lot of money to just buy a suppressor.

From what I have seen, you wouldn't want to use one for hunting of any sort. The only available models I've seen are military contracted weapons, the suppressor is mounted to the muzzle of a 12ga 500, looks to be about 4.5" diameter and 10-12" long. It is designed to allow the covert implementation of "riot" shotguns, however, the extreme size of the suppressor kind of limits the capabilities of the weapon, since you change from a Tactical length gun to a full length goose gun. (14"-->26" bbl)...not to mention the extreme weight of the device's effect on muzzle control in a close quarters combat situation. I grab that thing and you're not going to be able to control your own gun, and good luck swinging it quickly. But that's how I feel about it in combat...

Back onto hunting/harvesting. If you're able to legally cull this herd and this herd is legally established and zoned, the neighbors can complain until they're blue in the face and they have no power.

As far as hunting with this thing, I've HEARD that these are only effective with shot, and don't pattern very well even then (although tighter than the original 14-18" bbls) and perform rather poorly with slugs.

Not to mention that the rounds must be under 1100fps, otherwise you've still got a sonic boom that can't be silenced, which limits the power of your weapon. Typical 12ga 1oz. slugs run between 1500-1800fps, you're going to have to sacrifice between ~30% and 45% of your power to bring it down to sub-sonic levels. That's not as much of a problem in power as it is in accuracy and trajectory.

Personally, I'd either get a 20ga with slugs, or a relatively quiet rifle round (.357mag, .44mag, .30-30, .243 etc) and put up with your neighbors complaints if there are any.