Piss in her yard.
Feed the dog Hershey chocolate bars till it dies.
Take a dump on their from step. Or better yet, on their dogs. Take Exlax first though.
Don't hurt their dog!! It's not the dog's fault - it's the stupid owner's fault. Are there leash laws where you live? Can you put up a fence to keep the dog out? Have you asked them to please keep their dog away from your property?
Killing the dog or harm it should be difficult because
I suppose that when the dog is out, your neighbor is "watching" it or at least, he is at home. I have a idea. Find a dark spot in your neighnor's yard qhere you can hide without being seen. Get your hand on, you know the stuff hunters use to lure female, I think this shit it is female horse's piss or that kind of stuff. Anyway, get your self on some "HUNTING SCENTS & LURES", yeah that's it and wait for your prey. Spread generously the dog when you think
you won't be caught and enjoy. Try to not spread it on you, this stuff stinks for month.
Get yourself black clothes and something to hide your face.
Pay someone to do it.
If you can kidnapp the dog without you neighbor notices it, you can do what you want with the bastard and mail the guy his dog's ears or eyes. That's kinda sick. Go with the lure.
make a salt water solution. put some salt in a spray bottle. Take walks at night and as you walk by spray the salt water on their car. Over a month rust spots will develop on the car and no one will have a clue why it happened.
To reply 2 and 5:
SHUT UP! To the maker of this post: Dont listen to them. Dont hurt/kill the dog its not his/her fault. As you can tell, I am a total animal lover and if you did that, its not only that the dog would stop peeing in your yard, but you would feel ashamed. You'd feel worse than you ever had.