As I recall, it is not illegal to hunt or trap coyotes in Georgia and there is no "season" for it. IMO, what you need to be concerned about is (under state law) discharging a firearm within 150 feet of a state road and/or any city or county additional restrictions. If your neighbor is shooting a 410 with shot at them, then I'd say do that and try to be a better shot. The fewer shots the better.