Your neighbors should come live over here in Thailand and they'll soon get used to living with all types of neighbors. There's just no way on earth any Thai family would get rid of their chickens, or even their roosters simply because someone in the area doesn't like the sound of them crowing. It's very much a matter of live and let live over here, and while it can sometimes get to you, it works both ways.
My neighbors over here are not Thais and neither do they live here permanently. They only come for three months of the year and when they were here last year, they complained about my goat making a noise in the mornings (she calls out a little bit when it's feeding time), and then they complained about one of my dogs barking (no an excessive barker). Of course when they come over later in the year, I don't doubt they'll have something to say about the fact that I now have chickens. My point is I actually live here, and there is no way I'm willing to change the way our family lives just in order to please someone who only uses their home as a holiday house. The way I see it is if they wanted total solitude, they should have bought a house in one of the walled developments. Oh, and I have told them so by the way.
If your neighbors don't want to live next door to people who have chickens, then why the hell don't they live somewhere where it's not allowed.
Anyway, good luck.