My husband said that a BB gun will work with a squirrel, but you would want a break barrel BB gun.  It's pretty powerful and does the job well (almost the equivalent of a .22). We have tried the metal live traps baited with peanut butter and it doesn't seem to work, but maybe it would for you. 
If either of those don't work, my husband says that you can get a bag of peanuts and throw them out in the neighbor's yard. :)

I always follow a shot of wild turkey with a squirrel chaser.

I like all these great suggestions!  We have Wild Turkey here at the liquor store, but not the two legged kind!  The property on which we have made an offer has some huge trees and dense shrubs which harbor all kinds of critters, I'm sure!  It's hilly and rural, and I know coyotes will howl joy at their kills!  I used to think they were pretty stupid announcing their presence so loudly until I found out they are rejoicing over their prey!  The acreage is fenced, but I might consider those electric fences within the property too.  Not worried yet.  Short sales take a long time for approval IF it ever comes.

JD feels like Sue.  Travel is king.  Kids are gone!  He doesn't want anything tying us down. 

I bookmarked that Kania trap.  I loved reading the testimonials. 

Thanks for all the great answers!
Suzi

Tree squirrels got sooo bad...any plant in ground or in container was dig up and discarded.  Never let them win!!!  I cut up sections of rabbit fence...usually 4 or 5" by 3"....work into the ground/soil around the plant, sharp side up.  They won't dig in that but a minute...lol  Also works for rabbit that dig up plants to borrow under.  And I have a wired haired fox terrier aka rat on acid.....lol  He's fast and has killed his share vermin.

I hate to be mean but they ripped up my siding and got into my attic,want a mess,i hate them.Tree rats thats all they are,rat traps,and peanut butter works,or one big cat.

My neighbor sprinkles used (without the solids) kitty litter around his garden,
and the cat urine seems to keep most of the varments away!
They come to my yard garden instead! :(

I used to feed the birds until the hawks started picking off the Morning doves.
that came to eat.   feathers everywhere, blood on the roof!
After the birdseed started attracting mice, and chipmonks, then a huge rat!
I stopped feeding them.

I just rescued a little kitten just before Christmas,
He uses a lot of litter! I'll keep you posted!