Are you being serious? I can't believe you're actually considering killing a cat. I know as a child, I would have preferred to have played indoors in the knowledge that my parents didn't maim or kill animals, than play outside happy in the knowledge that they kill other peopel's pets. It's ludicrous.
Keep a water gun by the back door and when they come in, squirt water at them - this is how a responsible cat owner would repel their pet from doing something naughty (biting, scratching furniture, etc) so I would think that it would work in this instance too.
Also, there are zillions of cat repellants out there, I think the most effective ones are citrus.
http://www.martleyelectronics.co.uk/cat_control.ht m#crystals
Try googling "Cat deterrent", loads of suggestions will come up and unsurisingly, none of them involve killing an animal because it's utterly ridiculous and downright cruel, what if someone was to throw a stone or something at your child because they were causing a nuisance by making too much noise in the garden? Would that be fair?