The Dog Poisoner's Handbook
I'm sure the OP is no longer reading this thread but there are plenty of people who are still asking for help so here's my pennyworth of advice.
It's pretty easy to get away with killing a dog so long as you're careful. That's because the nuisance value of the dog is in direct proportion to the stupidity of the owner. Do a little internet research and you'll see that there are many idiots who just don't realise that their dogs annoy people. I've seen discussions where people tearfully write "Someone tried to poison my dog!" and anyone who interrupts the pathetically sentimental outpourings of sympathy to suggest that perhaps the dog was annoying someone nearby is subjected to torrents of abuse. "You'll be killing kids next" is the most common, followed by "How could you hurt an icky-wicky lickle doggy? I'm going to kill you!"
So if a dog's annoying you, you can be almost certain that the owner won't suspect you if you kill it UNLESS you have said something. Then you'll be marked down in their books as a dog hater and your hands are tied.
It takes a while to realise that the dog that is going to drive you mad is a serious problem. It's in the early stages that most people (as I did, the first time) make the mistake of going round to see the owner and trying to be reasonable.
The owner won't be reasonable. They'll at best make vague promises they won't keep, at worst be hostile. So SAY NOTHING! Don't swear at the dog (difficult I know); don't even look at it nastily. Certainly don't call the council or police. Grit your teeth and pretend that it doesn't bother you, so that if the problem becomes really bad you can poison the dog.
If you're above suspicion you can keep trying until you succeed. The owner loves his/her pooch so much that he'll think that anyone who's trying to kill the dog must be a psycho and you'll be in the clear. So long as you haven't communicated your dislike of the dog IN ANY WAY. It's best to pretend you like it though that's certainly not easy.
Slug pellets in sufficient quantity will kill a dog as will rat poison, antifreeze or ground glass mixed with meat. Yes it's cruel and inhumane but your needs are greater than the dog's so tough luck Snuffles.
Don't forget: Always buy materials out of town; PAY CASH for them and buy them somewhere impersonal; get rid of excess materials and packaging in a dumpster/skip a long way from your home; use gloves to avoid fingerprints and above all, NEVER say anything to anyone.
Good luck!