Some thoughts on this from a veteran of the rural dog wars:
Yes, it's an unhappy thought, putting down someone else's pet. Yes it's not the dog's fault, it's the owner. And yes, you can try the "nice" methods, to teach the dog to go bother somebody else - but are you really doing the dog a favor? (Not to mention the other neighbors who will be the benefactors of your niceness?
I'm sorry, but the simple, effective solution is three steps:
1. Notify the owner (excellent post above - look them in the eye and tell them you won't put up with it).
2. Notify the authorities (animal control or sheriff).
3. Dispatch and dispose of the animal.
What you do after that is up to you, and probably depends on how you get along with your neighbor. Tell him, or don't. My local sheriff advised shooting the offending dog (was killing chickens and chasing calves) and throwing it into the neighbors yard. I elected not to go that route, figuring it led to speculation that it had been shot there. Instead, I buried the mutt right behind the chicken coop he so dearly loved. My wife baked the neighbor a Christmas cake, made from farm-fresh brown eggs, and he never complained about the dog.
Dog hater? No, have two of them. Harsh? Maybe. But I got over that sentiment while taking my little girl to the ER after being bitten by a repeat-offending German Shepherd. Now there's a case where I would have shot the dog in the neighbor's yard, but the neighbor did the right thing before I got there.
Loose dogs happen - be a neighbor and return them. Loose dogs causing harm to people or other animals are dangerous, and should not be tolerated.