If those options don't work, you may want to consider speaking with the neighbor about having an enclosure for the cats built. This way kitties can go outside without causing issues for neighbors.
Many enclosures can be accessed by an unused window or doggy door setup and they can be very nice, depending on how much room you have.
Here's a site with examples of enclosures, from small to large and elaborate:
http://www.catsofaustralia.com/cat-enclosures.htm