Second, from now on, try to collect evidence. Set up a camera to video tape and record your back yard, how the dog bark, and how you negociate with your neighbour (when doing so, be nice).
Do this for several times if the dog keeps barking.
If the dog continue to bark, you have several choices:
1. just go to court and ask the court to stop the dog from barking (I guess there are special equipment for doing so) -- (american way)
or
2. show the tape to your neighbour and ask them to stop the dog from barking (non-american way)