Post a sign and indicate what is going on. "Please keep your pet off of the lawn". Advertise your frustrations to the neighbors, that way and if you know the culprit, kindly p/you the droppings place in a bag and place on the owners door step! THEY WILL get the hint! If not, call your local code enforcement office (I am sure there are leash and trespassing laws in your area).
You give them a treat every time they don't poop on your lawn and maybe they will be nicer and not take a poop in your yard