I've been in the same situation. My dog was on a food trial to see if she had a food allergy, and she kept getting cat poop, so I had to start counting from day one again! I asked the owner to keep the cats in at night for a month, and he simply ignored me. I called animal control to ask what to do, and here is what they suggested.
If it is in a flower garden, you can bury chicken wire just under the surface of the garden. Plants will grow through it, but cats will be deterred from digging (and thus pooping) in that area.
You can also bury plastic forks in the garden with the tines up, but that seemed like of labor-intensive to me. You'd have to use an awful lot of forks!
They told me that vinegar actually doesn't work. You don't want to use anything inside the yard that the dog could get -- moth balls & cayenne were suggested to me by others, but I don't want my dog getting into that!
Orange peels around the perimeter of the yard can deter them.
For about a $100, I found a motion-activated sprinkler online that you can hook up to a hose at night, and that should keep them away.
If the cat doesn't belong to anyone, trapping it is also an option. You can get a fairly inexpensive humane trap at Harbor Freight. Home Depot also has them, but they cost a bit more. Animal control will usually pick it up, but you have to find out their hours and regulations regarding trapping. They often have a trap that you can use, but there is generally a waiting list.
What I ended up doing was sprinkling some boundary repellant outside of the yard on the perimeter of the fence in the front, which is how the cats were coming in. You can get it for about $7 a can from PetEdge (cheaper than a pet store), but you literally have to put it down every single day or they will come back. The back has a warning to wear gloves and prevent pets from ingesting it, so I wouldn't put it anywhere where an animal could eat it. Technically, all cats and dogs should avoid it because it does repel them, but I wouldn't take any chances. I was far enough from the road that putting it outside of my fence was pretty safe. Honestly, though, if I let up for a day, the cats were back.
If they are digging in flower gardens (my neighbor's cats were not -- they were just pooping on the grass in the yard & not burying it), pea gravel, larger rocks, or large bark mulch can also deter them. They love regular mulch.
I have used a capful of household ammonia on garbage waiting for the trash man and it keeps all animals, dogs, cats, racoons etc out. It's cheap but I don't know how often you would have to reapply as I only use it one day a week on trash day.
I like the idea of trapping them - and turning them over to animal control whether they belong to your neighbor or not. Then the neighbor will be held accountable.
Well, Nancy, I confess that I did run a trap for a while just because that neighbor was such a jerk. Alas, the only cat to get caught in my trap was not his. They were too smart. The only one I caught had no tags, no collar, and might have been one of the local ferals. I gave up on trapping because I wasn't very successful.
You run the risk of ticking off neighbors. They'll see which house animal control comes to when Fluffy disappears because word gets around! I went with the boundary repellant, but I wish I had sprung for the motion-activated sprinkler.