DDorphins - I don't have a problem with cats eating squirrels. But here in CO, squirrels carry ticks that carry bubonic plague, and I'd rather have squirrels than plague. We do have a couple of falcons that keep the squirrel population in check for the most part.
But what I've done to keep the squirrels in my yard in control is feed them. I have a couple of feeders that I keep filled with el cheapo bird seed that's mostly cracked corn & sunflower seeds and they seem to keep out of the other feeders & don't dig. I also give them the heel of the bread I make every Sunday, so they seem quite happy about that. I only have 2-3 squirrels at any given time.