Get an air soft rifle. Air soft rifles use plastic pellets. It is used in air soft games and shot at people as part of the game, so it will not kill the dog but will sting him when he gets hit. When shooting at the offender be sure to put weapon in automatic, then pull the trigger, spray and pray. This will discourage the dog and the homeless from using your lawn as a restroom. Hope this helps, but if it doesn't at least you have the pleasure of hearing the dog yelp as he does his business on your nice lawn.