We had a problem as we have a corner lot and peopel think that the property on the far wall is common area and walk apparently large dogs judging by what is left behind. I am with one of the other posters about being direct. I even once picked up the dog poop and left it on the offenders door step each and every time until they got the message. For some reason they did not want to come out and "discuss" it with me.
However in the last place we lived we found out that we could not do anything about dogs on the easement as we did not own that land and therefore it was not private property. Ever try to call a cop when a dog starts pooping and have the cop arrive in time to see it happen. it is a losing situation and I found that if I returned what their dog left behind they had nothing they could say about it and would choose some more passive homeowner's place to walk their dog.