If you are at all cordial with your neighbors I'd say talk to them and at least suggest the fires be lit earlier in the evening, under parental control, with appropriate safety measures, not during a burn ban, and away from your property. If that doesn't work I would call an insurance company and find out what happens if you set a fire on your porperty that burns down your neighbors house. I bet that answer would make them sit up! If your not comfortable talking to them, or they are non-responsive, I'd call the FD and PD. And do it before the fire gets too big, b/c once it gets loose it is becomes very difficult, time consuming and dangerous to put out. Especially at night. It is unbelievable how fast these things spread in dry weather (thank goodness for your recent rain).
I'm a volunteer FF and, unfortunately, in my district, we don't fine people. Then again, we've never had anyone who re-lit a fire after being told to put it out. Even if you don't want to report them, you can call and find out what your laws are and what the FD can do. Another course is to go to your Town Board (or whatever municiple gov't you have) and see if they are violating any laws.
Good luck!