The Animal Control Officer came and we had a nice little chat. After he left my house he was going to the owners house for a not so nice chat. We could have had them cited and went to court, but we realy want to be good neighbors, so we opted for a warning.
The AC Officer was very informative. He said that in Georgia we have the legal right to protect persons and property (we already knew this ) and that if the dogs were attacking our livestock we were within our legal right to shoot them, then call 911 and make a formal complaint/police report. He said the big problem is when someone shoots a dog and tries to hide it.
We will take his advice - however shooting an animal that is attacking another is risky business. I'm afraid that I'm not a good enough shot, but my son is

So we have a viable option -- if the neighbors aren't responsible.