Others have said it, but I will stress it again: do not let anyone see you shooting ANYTHING within city limits!
Crossman 760. They’ve been making them for decades. Its a pump - no CO2 cylinders. Pump it 10 time and hit the varmint with a pellet and thats it for the critter.
Its cheap, too - $20-$30.
However, try a Have A heart live trap....they work great when baited with peanuts.........then dispose of the squirrel any way you want.
FWIW, I caught 4 squirrels and a possum in the course of a week two weeks ago in my trap.......
I have a Sheridan pump. Accurate, affordable and quiet.
And a .22 CB or BB round will do the same job at about the same noise level.
If you’re a lousy shot and noise isn’t a concern, a Mossberg 12 ga with 00 buck is a good choice. You may have to relandscape, however.
Whatever solution you choose has to overcome the reproduction curve. That is, it has to eliminate the squirrels faster than they breed.
One solution might be a “death barrel”, with a fast, spring lid, so that when the squirrel goes for the bait, they drop into the barrel. The bottom of the barrel is charged daily with carbon dioxide from vinegar and baking soda. So as soon as the squirrel drops and hits the bottom, it suffocates with its first breath. Since CO2 is heavier than air, the barrel will stay charged until the dead squirrels are emptied from it.
Quick and painless, and the lid can be secured until the squirrels get used to jumping on it.
I have a RWS .177 pistol it is very accurate and has good velocity with penetration into pine lumber of about a inch. I do think the Sheridan pump would be a better choice. My only advice is aim for the neck.
They're not silent either, they have a very noticable loud "snap" and considerable recoil. I've dropped rabbits with head shots at about 100 ft.....
Here's the Link: Kodiak
I am also an urban squirrel hunter; welcome to the brotherhood.
You have much to learn, grasshopper, before you will attain greatness in this area. By "greatness" I mean "not getting arrested". That is the most important priority. Many times I have ensconsed myself in my backyard blind, beer and BB gun in hand, only to hear the neighbor kids come out and play; I won't hunt if there is activity nearby, especially kids, so I defer my hunt until later. That in itself is a big discipline that I am thankful for achieving. I lacked it before.
Beeman in either .177 or .22
"License to kill gophers by the government of the United Nations. Man, free to kill gophers at will. To kill, you must know your enemy, and in this case my enemy is a varmint. And a varmint will never quit - ever. They're like the Viet Cong - Varmint Cong. So you have to lie back on superior intelligence and superior firepower. And that's all she wrote."
Be careful. Some cities don’t even allow you to trap small wildlife like squirrels — much less to kill them.
I just remembered this article from 1984. (No, I don’t have a life)
http://www.minisniping.org/articles_petercapstick.html
Capstick was a noted big game hunter and author.
Use a wrist rocket to knock them out of the tree, and a big dog to catch them after they fall.
It’s fun.
The Benjamin air rifles are powerful and inexpensive (I own a Sheridan), but they’re too loud for your purpose. If you’re going to own just one pellet rifle, consider the RWS Diana in .177 cal. It’s a bit pricey, but you’ll be proud to own it.
I’ve never owned a side-lever type, due to paranoia over placing my fingers in the breech of a cocked spring airgun.
.177 or .22? I prefer the flatter trajectory and longer useful range of the .177, but you may find either caliber fit for your purpose. Scopes are not needed for airguns, they seem more to get in the way.
I remember getting a solid hit on a fair-sized Grackle with my Diana .177, and walked over to examine it, picking it up by the wingtips. The body fell away, leaving me holding each wing by the tip, due the size of the exit hole in the bird’s back.
If noise could be a problem check out the Gamo Whisper .177 it has a noise dampener (works like a silencer). If you can get your hands on a July 2008 edition of the American Rifleman (NRA magazine) it has a very good article about the Gamo Airguns starting on page 42.
On line Cabela's and BassPro both show several different air rifles.
Whatever gun you end up getting, make sure you get a scope designed specifically for airguns. Airguns recoil differently than firearms, and will destroy a scope made for a firearm.
The girlfriend feeds her squirrels. Those and the Cardinals, doves, hummingbirds, blue birds, Blue Jays and finches.
Her dogs just ignore it all.
She had a bald eagle sitting on her air conditioner unit a couple of years ago.