[Jeff Higgins]

A standard, unmodified Benjamin 392 will fill the bill. $200 from Airguns of Arizona. The 392 is .22 caliber, they also make a 397, which is the same rifle in .177 caliber. The .22 caliber is far better for squirrel control.

Like most things in life, of course, the sky is the limit on air rifles. I really got into them in the early Obama gun panic years, when firearms and ammunition were all but unavailable. I figured a quality air gun would "get me by". Hah - years later, I have quite a collection of them. Far from just "getting by", they are a very interesting and enjoyable pastime in and of themselves.

I have four pump guns modified by MAC1 as mentioned by Vash. Two vintage Sheridan Blue Streaks, one of which I have owned since I was about ten, and one purchased off Gun Broker a few years ago. The other two are modern versions thereof, one a Blue Streak and one a Benjamin 392, which are now identical to one another (the Blue Streak was discontinued a few years ago). These are very powerful air rifles, exceeding 20 foot pounds of energy with a full charge. They are, unfortunately, very loud. This may or may not make a difference. Neighbors proximity becomes an issue.

Every bit as powerful, but far quieter, are the quality spring piston guns. I have a variety from RWS and Weihrauch that will match the power of the pump guns. These are not cheap, however, running into the $300 - $600 range, or more.

And yes, scopes are a big problem on the spring piston guns (but not on the pump guns). The reason for this is that they recoil forward when the piston hits the end of its travel. Scopes that hold up to really heavy recoil from conventional firearms will fail on these rifles. You have to make sure that whatever you mount on one of these is "airgun rated".

I have had great luck with Weaver scopes meant for .22 rimfires. Weaver does rate these as "airgun compatible", where they do not give that rating for their centerfire rifle scopes. Forget the cheap $100 or less "airgun" scopes from companies like Leapers, UTG, Hawke, Umarex, etc. I have never had one hold up for long, even though they are "air gun rated". You do have spend some money if you want a scope, unfortunately, at least for a spring piston rifle. Not so much for a pump gun, though. They are very easy on scopes.

Anyway, a pump up Benjamin, with its open sights, should work just fine of squirrels. Assuming you can use open sights well enough to hit them properly, the rifle will have all of the power you need. There are scopes and mounts available, should you need them.