MIne may not be a popular opinion, but pump the gun all the way up and land a pellet in their earhole or at the inside corner of the eye. They don't run very far with that treatment, trust me. Living in the sticks, we have a HUGE feral cat problem. There are neighbors around who put out buckets of food for any and all cats. Add to this the number of townies who drop off litters of kittens on the roadside.
Many people forget that while cats have been domesticated for thousands of years, they have NEVER lost their hunting instinct like MOST domesticated dogs have. Cats kill and seem to truly enjoy it. Beyond the songbird problem, which isn't a huge issue to me personally, they also kill a fair number of rabbits and can and will take a young game bird if given a chance. Looking objectively at this, it shouldn't just be legal to kill cats, it should be MANDATORY. Feral cats are bad news. If your neighbors can't take care of their pets, do it for them.