WHY DO DOGS BARK:
1) Need (
water, food, companionship, cold, hot.....)
2) BOREDOM AND LONELINESS that soon breeds anxiety and paranoia about the tiniest noise.
3) Protecting territory from invading animals, and other perceived intruders.
1) Make sure the dog is not truly in need of food, water or
shelter. First address the basics, does it have housing, food and water? If not, document for several days (supplement food and water) then If this is a case of neglect provide for the dog through the
fence and call the authorities (SPCA, Humane Society, Animal Control etc.).
2) This is likely a large component of why this particular dog is barking. It is scared, lonely and bored, if not also hungry, thirsty, cold/warm. If the basics are taken care of, then it is mental abuse (lack of companionship, attention, boredom etc.) and you can offer to fill this void by walking the dog, providing attention and companionship through the
fence, toys, treats etc. Again, I get that this is not your dog, but it is a potential solution.
3) We want them to bark, within reason, to alert us to trespassers of both the human and animal sort, but we need them to understand that their message has been received, thank you, and we no longer need a warning about that particular thing at this time. This is a training issue for both humans and dogs. Dogs are like a three year old child, they need to know you heard them, understood them, and are taking steps to deal with what they are trying to tell you - like when you are on the phone and your toddler keeps bugging you "Mum...Mum....Mum....Bobby's bugging me...Mum...Mum...MUM!!! BOBBY'S BUGGING ME!!!". Until you actually acknowledge the child, look them in the eye and give them your full attention and deal with the issue, they keep "barking" at you. Same with the dog. Acknowledge them, "go and see" what they are barking at, THEN tell them they are a good dog, but that everything is fine now, thank you for letting me know. This is how they learn what to bark at, when barking is acceptable, and how to not become a mindless yapper. We must teach them what to notify us about, reward that, but do not ignore barking or just yell stop, do them the honor of investigating what they are trying to tell you about, respect that they feel this is some sort of danger, then educate them as to what is appropriate to alert you to.
Obviously first step is to try to get the owners on side and have them deal with the issue...but reality is such that most folks will not respond well, or at all to such a request. That said, lie through your teeth, tell them how adorable their new dog is, blah, blah, blah and then apologize for being such a light sleeper (or it wakes the baby....blah, blah, blah) and that you know you being a light sleeper is not THEIR problem and you ARE using earplugs and white noise machine....but if they could perhaps help you...... Yeah, I know, what a bunch of BS, but make it YOUR problem and ask for their help, it usually works out better than 'SHUT YOUR DAMN DOG UP' which will just make them defensive, argumentative, potentially aggressive and for sure, unwilling to deal with the issue, just to spite you.
OTHER OPTIONS:
Dogs "disappear" all the time from "bad situations"... speak with
local rescue groups and see if you can find a placement for a "homeless dog, running at large". Then have it disappear (best when they are at work or overnight) and rehome it.
Most areas have some sort of noise bylaw, as suggested by some others, start keeping records: log barking time of day, length of barking, frequency of barking. Take photos/video of dogs living conditions, video dog barking at all hours of the day and night. They don't say a picture is worth a thousand words for nothing - video is likely worth millions of words!!
I understand this is not your dog, but it may as well be with the lack of attention they are giving it - it will likely be up to you to train it as to what is appropriate to bark at, and what is inappropriate.
As a human, currently owned by 11 dogs, I am very anal about my dogs not being disruptive to the neighbors (we are on tiny half acre lots). On top of that, they are primarily Miniature Pinschers, who are notorious for barking (around here birds over head, smoke from the neighbors burn pile just to name two of their perceived territorial intruders). I have tried several of the ultrasonic units that you "hang" outside and are battery powered, they run around $50 but can be had for much more and much less...and they do work, but only initially, in my
experience. It seems within a week or so they become immune to it. One lasted a few weeks, but boom, tried new battery, just in case, nope, they just no longer care. My two friends tried them with their MinPins, one had the same result as me, the other turned it off after a couple of days and just has to bring it out and the dogs stop barking - but it must be used sporadically, and of course is useless if they are not home to wave it about.
I do use bark collars on some of my more neurotic dogs - the ones who start barking and then become so hysterical they just can't stop. Of course, this gets the others all freaked out and barking (I call it chorus barking) because if one thinks there is danger, well, heck, all the others better join in, even if they have no idea why dog 1 was barking in the first place. Interestingly, the collars have actually IMPROVED the life of the barkers by stopping them before they become hysterical and freak themselves out even more!! They now have the ability to assess noises and danger (even with the collar off) before becoming hysterical.
The collars I use are a dual system, bark and vibration activated, and increase in strength with EACH bark up to a level ten. This allows them to bark two or three times, before collar activation bothers them. They can still speak, they just can no longer "yell" hysterically. With each bark, the correction zap intensifies. I know this sounds cruel, but we tried it ourselves, it is equivalent to the static shock we got as kids from shuffling on shag carpet. Not painful, but certainly not pleasing or something one can just ignore. The intensity is up to the dog, them more it barks in a row, the greater strength to the zap. There is one drawback, some dogs learn the secret of spacing their barks so that the collar intensity is not affected - it resets to zero after 5-10 seconds!
You can also get remote collars that put the zap power in your hands. I personally failed with this method as I was not consistent with the correction, and just ended up confusing the dogs more than anything. But a more dedicated person may find this works better for them.
Bark collars are NOT cheap, and you do get what you pay for with this item. If this is a route you are thinking of make sure you factor in the cost of powering the collar...some are rechargeable (but then you need two, otherwise the collar is on charge every couple of days and dog has no collar), others are battery operated (the PetSafe collars I use have a proprietary battery that costs $15 each!!) but often there are "battery hacks" on line that can lower the cost of replacement batteries.
Oh, and again, nice as pie, let them know regularly that the dog barking is STILL an issue. My neighbors didn't, I heard about it at from the local
feed store clerk who warned me my neighbor was choked! I thought the problem had been dealt with (no barking when we were home) but apparently when we were away (rarely) the dogs would go barking mad. If I had known this I would have dealt with the "away barking" much sooner.
GOOD LUCK!