Trouble with neighbors dog...

Check your local ordinances.
In my county you can shoot and kill a dog if it is a danger to you or your pets.

If you get caught simply shooting at a dog for being in your property, you can go to jail and get fined big time if it is not posing an immediate threat. (thanks to bleeding heart animal tards who must have never been attacked.)

I would notify the neighbor of the situation and hope they will not act like toothless rednecks that will immediately puff up their chest and call their next of kin for a night vision crossbow a-thon in your back yard to retaliate because their psycho dog is more important than the safety of others in their eyes.....yes there are people like this in the world and usually people that own aggressive dogs like this are total social douchebags.

If they act like asswipes about it then call the local animal control officer and have them come over to talk to the neighbors and make sure you file a report to get it on record.
If they are asswipes about it then expect to have lingering animosity with said neighbors after animal control speaks to them.

My neighbor had an aggressive dog and I recently tried something I never tried before and it really put the dog in it's place and turned it into a scared kitten every time I do this.
The dog would bark like mad when anyone was in my back yard and it would charge the fence as if to kill someone, barking like a friggin rabid demon from hell.
So one day I decided to give it a blast with one of those small sporting event air horns and boy did it scare the living crap out of that dog.
It ran off, tail between legs sideways and crashed into his dog house in a panic. ha, ha, funniest thing I ever saw.

The dog literally was so freaked out that it did not come out of his dog house for 2 days.

Every now and then the dog would start barking like an idiot non stop and I would shoot a quick blast out the window and the dog would immediately STFU.

Now if we are in the back yard and the dog comes around and even hints like it's gonna get agressive I reach into my pocket and the dog runs for it's life...ha, ha.

Can't say this will work for every dog but it works well on the neighbors idiot pitt bull.