i went through the same thing a couple of years ago, after a while it got so bad that my cats wouldn't go outside & started poohing & peeing inside. this is when i got a mates paintball gun which worked very well & he never came back. there was plenty of people on here that weren't happy with that but hey it worked & the cat wasn't killed, it belonged to a neighbour.
the air rifle will work easily, i use mine weekly to kill possums but you do need to be a good shot as there is nothing worse than wounding something & not killing it.