50 cal's comments should be duly noted. Round balls, especially at low velocity have a real penchant for skipping off even the softest soils when you miss your target.
That being said, I have pretty much the same problem as yourself, only with Cottontail rabbits being the garden pillagers. I also have neighbors fairly close on all sides.
You didn't specify what caliber or type of pistol you are planning to use, so I can only tell you what I have had success with.
I use a 4 foot tall and 8 foot wide sheet of 3/4 in. plywood to stop any ricochets. Tests conducted at the range proved my selected load only dented a piece of 3/4 when I fired directly at it from 15 yards (many times the bullet rebounds right back at you, so be ready to duck, and wear eye protection). I then place a bait station of tasty veggies and a mix of shell corn and oats, directly in front of the center of the plywood, and use my shop window as a stand, from forty feet away.
The pistol I use is an old E.M.F. .36 caliber, 1858 Remington revolver. After measuring the distance the ram traveled into the cylinder, I added a quarter inch to that distance, and determined that 11 grains of fffg was the smallest charge I could use, and still have the ball compress the charge, and it is important that it does.
You can't see the bullet in flight, but the velocity has to be pretty low, because, many times it don't even break the skin ! However, when hit, they drop right on the spot, if you get the front half of the body.
Ground Hogs are a lot tougher animal than rabbits, so I would guess I would have to concentrate on head shots, though a body hit should, at the very least, make them crave someone else's peas ?
I have to warn you, there is no way the report of 11 grains of black powder can be mistaken for quiet.
