Check out this website and talk to them: http://www.tornado-technologies.com/
If I am not mistaken there is something like you are considering right on his homepage.
He is a good guy. I have had him thread probably a dozen guns that he threaded for me. Great guy to do business with.
Threading the gun is the hardest part of the project you are talking about. The suppressor is just a matter of buying it and doing the paperwork (which takes about 10 minutes).
EDIT: I see on his price list he mentions the Beretta 87 and not the 84 as far as I can see. This doesn't mean he can't do it however. Give him a call. I am not familiar with your gun: he has a picture of some smallish Beretta on his home page.
You know the rest. In the books you have read
How the British Regulars fired and fled,
How the farmers gave them ball for ball,
From behind each fence and farmyard wall,
Chasing the redcoats down the lane,
Then crossing the fields to emerge again
Under the trees at the turn of the road,
And only pausing to fire and load.
Last edited by 444; November 3, 2009 at 08:15 AM.