The dog is marking the bounds of it's territory so you have to deter it from doing so. There are several commercial brands of dog/cat repellents on the market but you can try one of the home made deer/rabbit repellents listed on the 'deer (something) forum' since dogs, deer/rabbits, smell before they do their "marking"/ eating.

Sometimes this works (I know it will probably bring some real howls from readers), but have a male friend (or pour urine) twice the height of where he's capable of marking. Then spray some hot sauce on the grass in a circle around the tree. Cheapest combination, works well. Alternative is the spray repellents from the store (but they can get expensive. The question might be: does it matter? Or is it just emotionally annoying? Have you tried talking to the owner of the dog? Or calling animal control?