Have you talked with your neighbor about this? Is he aware that the cats are killing birds? I'd hope that he would take responsibility to keep his cats off of your property.
If the neighbor will not take steps to keep the cats from killing the birds, check to see if your town has an ordinance about cats being outside. Some do.
Is the feeder close to bushes? Cats like to hide under bushes or other low vegetation and wait for birds. If you move the feeder farther from the vegetation, the cats will lose the element of surprise, which might give the birds a chance to get away.
Good luck. Please let me know if you have more questions. .
