Roosters are very territorial animals. They crow to mark their territory and warn other roosters off or establish their order of rank if there are several roosters in the flock.
The easiest solution would be to have all the hens living in one big coop together and reduce the number of roosters to 1. You'll still hear him, but much less constantly.
If your neighbor isn't willing to get rid of his excess roosters, he should at least divide his yard into clear territories for each rooster and put an opaque barrier in between. The remaining roosters will probably start a little crowing battle as soon as one of them starts crowing, but the lack of sight should calm the situation down after a short back-and-forth.
Living in close proximity with other roosters is a constant stressor. The "alpha" rooster will not stop intimidating the other ones in the flock, even if they do not challenge his status. And once one rooster starts crowing they will all follow, one after the other. Read here for more information.
The next problem arises if the area is too small or otherwise unsuited for the flock. You write "He's put up a few pens with chickens". If these pens are too small for the number of chickens, they get bored and cannot entertain themselves with scratching holes or anything. If you're lucky, there are local or national directives concerning how much space each chicken must have that your neighbor is required to follow.
Hens should also have free access to a hen house or any kind of hiding spot or roof in addition to a rail that is raised from the ground. If they feel like they cannot hide away from a bird of prey (therefore the roofs) or a land predator (therefor the rail) they may crow to warn each other of every little thing that seems remotely dangerous.
And lastly, roosters can crow if they're out of food and/or water. (source)
If there actually is only one rooster, you cannot expect your neighbor to get rid of it. Not having a rooster causes stress to the hens. And unfortunately, some rooster just like to crow constantly...
There are some tricks to stop them from crowing at night, but it's your neighbor who must implement them.
- There are stretchy fabric "no-crow collars" the rooster can wear around the neck. In a relaxed position the collar doesn't do much, but it restricts the air flow while the rooster stretches its neck to crow. It won't stop him from crowing, but is makes the crows somewhat quieter. (Source, see it in action here on Youtube.)
- He should entertain the chickens by hiding the food under a thin layer of straw, hey or shredded paper or by feeding corncobs or big chunks of vegetables that have to be picked apart. You can even craft a very simple puzzle feeder for chickens by wrapping some treats in pieces of paper. Here's a list of commercial and DIY chicken toys.
- He should lock all chickens onto the hen house at night and block out as much light as possible.
- He could also put the rooster into a box at night that's just a little too small for him to stretch fully. Since roosters need to stretch their necks for crowing, they can't to so in a too little space. Make sure the box has air holes, though! (source: last post)