Airgun Pistols - Some Choices to Use
Crosman 1377 - A venerable design that has been taking game for quite a few years. Unfortunately, the 1322, it's .22 caliber sibling, is no longer available. However, you can convert a 1377 to a 1322 if you like with a few parts. This gun has the advantage of being adjustable in power by varying the amount of air you put in the gun. Another advantage is that it is less susceptible to cold weather side effects that you get from CO2-powered guns since it uses air.
Crosman 2240 - A great little bolt-action pistol that runs on CO2. Accurate, compact, and infinitely customizable with lots of aftermarket parts. Velocity of the .22 projectile is adequate for squirrel and rabbit sized game at reasonable distances, and you get a decent shot count from each CO2 cartridge/powerlet.
Crosman 2300 Series - An upgrade to the 2240 platform, this gun features a great rear sight and semi-custom front sight, as well as a metal breech that lets you mount additional sighting options. The trigger is better on this gun than the stock 2240 as well. However, I believe it is only available in .177.
Benjamin Sheridan Pneumatic - A pump-up airgun similar in function to the Crosman 1377. This gun lends itself less to modification, yet in stock form is quite capable of taking the size-appropriate game of your choice when you do your part and put the pellet on target.
Benjamin CO2 pistol - Similar in function to the Crosman 2240, this gun also does a good job on small game. I prefer the sight system on the 2240, but the Benjamin sighting system is quite adequate for the hunter if not the target shooter.
RWS 5G - This spring-piston pistol is powerful and accurate. Self-contained, all you need is a pocket full of pellets and you are set for the day in the field pursuing your intended game. There's no nonsense about this pistol!
Now, are there other pistol offerings out there that will help you with pest control? Certainly, you can use whatever pistol you have that will hit the target with adequate force. However, if you intend to actively pursue small game, and not just pop the occasional pest, then I believe these candidates are your best options. And airgun pistol hunting is among the most challenging of the shooting sports. You really have to work at it when using an air pistol, so get the right gun for the job before heading out into the field!