There are some very nice air rifles that are accurate and can be scoped for even better night shooting. Quiet, and more than enough to take out squirrels. 

Or you can get a barn cat.  A cat that may or may not have been feral but lives outside and hunts.  Groups have them just to get the cats a place to call home. 

 Legal, they hunt at night while you sleep.   All you do is give them a place for shelter, water and food, but not so much they won't hunt.   Outdoors, they are very little work. 

My daughter had two cats, so I ended up with two cats.  They are doing a wonderful job.  I have a planter of blueberry's and one sleeps in the bed. 

So my yield has increased with them on the job.