Well, if the neighbor is aware, and does not care about it bothering other people, I think the only option here is to actually call a higher power to deal with the situation.
Best plan with there.
Otherwise you'll just make some tabloid news about a silly dispute gone wrong...might air on Fox though!
or
Play some loud opera every time their dog is out...or...get the whole neighborhood in on it, so when the dog barks, evryone blares the opera...or drives over with their cars and honks relentlessly so they get the message....
Of course it could easily backfire as it will show that they are in power and you're reacting to them...