No offense Mr. Mullins, the environment in which you describe (your residence), its close proximity to neighbors and your pest problem is not conducive to the employment of an airgun to resolve your situation. In fact it could very well lead to disastrous consequences. Should you reside out in the country side, that would be an all together polar opposite scenario.
I have used squirrel traps with fantastic success for years; it is all about the bait used I.E. Try oats, grain or feed and keep your scent off the bait and trap. As far as Coyotes - they may very well thin once you have a handle on the squirrels and then again they may not. Get a hunting dog, they are smart, make wonderful companions & protectors for your loved ones as well as alerting all who are near when a Coyote is present.
Now let’s get to the fun part. You want an airgun - if it were my first go around I would be listening very closely to what wisdom Mr. Cannonball so graciously shared with you. The Eastern European Bloc guns he mentioned are an exceptional value; ruggedly built, accurate and dependable.
Sound like an old man who has an opinion “ I know opinions are like a—h——- everybody has one”. Take it for what it is worth I mean No disrespect. Experience is a byproduct of age. Never, at any cost, permit negligence to endanger the lives of others.
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