I love this forum. Someone who actually understands predator/prey population dynamics. Here in MI, if there are no deer/rabbits/etc, it's because there are too many coyotes. Most don't realize that if there are no deer/rabbits/etc, then there wouldn't be any coyotes, because they'd of moved on to more lucrative feeding grounds.
I've been going out after squirrels the last few weeks, but like you, i end up just spending the day stump shooting. In retrospect, I consider none of those days where a squirrel didn't fall to be a failure.