Now it won't work for all situations but if you can get your hands on the dog or get near enough to it to spray it you have solved your problem. Everytime the dog comes in your yard give it a nice coating of buck lure and pretty soon your neighbor will start keep their animal up. You see buck lure is made to attract deer in hunting season and is made from deer urine so it smells like the dog has been rolling in something really nasty. Because it is made to attract deer it has a strong scent that will carry over a long distance. If every time the dog gets out it comes home reeking of urine and that little added musky odor that means that a doe is ready to mate... well lets just say that is one dog who will be force to stay home. Best of all you don't take the heat. Dogs naturally gravitate to smelly substances so unless someone sees you putting the buck lure on the dog you are not going to be held responsible.
There is also boar lure which works especially well in rural areas as it makes domestic pigs crazy. With either one the dog will make everything it touches... kids, clothes, carpet etc stink to high heaven and it has the added benifit of making other dogs treat it in a manner it finds confusing.
