Unfortunately, there isn't an easy solution to this one. Bells on collars are not a complete solution because often by the time they ring it's too late for the bird. Behaviour modification isn't going to work because you can't be there every time the cat hunts. Doing anything when your cat appears with its prey will only stress the cat out - it is too late for it to associate its hunting instinct with your displeasure. The only real way to stop the hunting is to keep your cat indoors or have an outdoor enclosure for your cat. Depending on the cat, this may be easy, or seemingly impossible. The Cats and Birds: Keep Cats Safe and Save Bird Lives [1] has some suggestions that might help.

If it is a neighbour's cat that keeps catching your backyard feeder birds, chipmunks and cottontail rabbits, try to situate your feeder so it is in an open area not too close to shrubs or things the cat can hide behind. If this is impossible, you can put a short wire fence barrier between the cat's pouncing spot and the feeder. This will slow the cat down as it will have to go around or over the barrier to get to the birds, giving the birds a little extra time to escape.