How would you prove which turd belonged to which neighbourhood cat?
Maybe If you stand in your garden for several hours with a camera you can get photographic evidence to present to the owners of the culprit,although I still don't know how you expect them to stop the cat doing it's business wherever it wants to.
I have never known a cat to poop in the middle of a perfectly manicured lawn anyway,they will do it in long grass and then bury it but not (in my experience of owning cats for many years) on a short lawn.