I have a RWS mod 34 Diana and it is a shooter. I take out pine squirrels at the tops of white pins without any problems. The gun is balanced and easy to cock and hits hard. You can spend more on a higher powered rifle but no need. Remember pellet rifle recoil is forward not back, so you need a scope that's designed to handle it, and once zeroed your tree rat issue will be gone. 177 is all that's neede but if you want a larger round go with the 22, just a bit slower in speed.
I have been a Air Rifle enthusiast for years. I own quite a few of really nice German/English Air Rifles, all
custom tuned. I also own a number of Co2's. I am a "Springer" shooter. Love them, understand them. I have shot squirrels over the years, although I hate it. (and ever since a Youth have been a avid hunter). But just killing these creature's that I love to watch and become attached to with their playful antics, etc. Yes, there comes a time when they over populate and you Have to thin then out.
First all You have to understand that they are tough. Chances of wounding one is very high. And then besides the sickening feeling you get, they will often run into the neighbors yard and you can end up with a whole lot of problems with the Police. You need to check your city/county ordances if you have close neighbors that might hate gun owners or some Pita type. I have seen almost every kind of rifle on this forum. I really disagree with many of the posters. And I WOULD NEVER ATTEMPT TO KILL ONE WITH A BB GUN. The 2240 co2 is one of the most modified guns out there. I have one, with a nice TKO shroud, that is totally a complete silencer. However
I only use for "Rat's. Just does not have enough power to kill squirrels all the time. And mine has a Walther Lothar barrel and extremely accurate.
If you are out to just kill squirrels then I would suggest to buy a trap and just relocate them. However, why not get into the sport of Shooting Air Rifles. This is a forum devoted to shooting. I could go one posting pages about air guns, but one thing caught my attention. The Post by Predator55. One of the best air rifles to get started with shooting is the
Diana Mdl 34. A gun that is well known to air Gunners and the first air quality air rifle that bought after so many cheap Walmart and Crosman rifles. German Made, great barrels, (a Whole Forum dedicated to just this one rifle), And cost for this quality is on the very low side compared to some I have. My last purchase was a Walther LCV which runs around $600-$750. The Diana around $250.
To answer the OP's post. He does not want to use a scope. The Diana was actually designed to NOT USE one. Many newbies will complain about the notorious "Droop" that is unique to them. However that design actually makes the the Diana one of the best air Rifles to use without a scope. And fun to shoot. Start off with a nice rifle and this will become a fantastic hobby. Springers are to me so much more fun than C02. They have LIFE, recoil, a one shot one kill gun. Yes they require training, they have a reverse muzzle flip. But once you train with them, they can be deadly accurate.
The Best most humane way to take out a squirrel with a Pellet rifle is one that shoot around 650 to 800 FPS with the right Pellet. And Head shots are always the best. Want a insanely accurate air rifle. Get the
Walther LGV like I mentioned about. About as smooth as any custom tuned gun I have shot and they shoot this way right out of the Box. Mild shooting, great trigger, and mine is mounted with a very lightweigh ClearRidge scope. Or start off with the wonderful Diana Mdl 34 with the open sights. (Scope can be mounted later with a special mount to compensate for the droop of the rifle).
Note, when buying a air rifle, do not get caught up in high advertised rifles that say on the Box at Walmart as 1000 fps. A pellet is much more effective and accurate at a FPS of around 650 for 22. cal and 750 for 177. My Walther shoots around 650 for 22.cal and my Custom Tuned Diana 177. around 750.