The Christian way to deal with this would be to bake some cookies and deliver them with a note. "We have moved our play yard at your request, and apologize for any disturbences our children may have caused. We look forward to being good neighbors." The Bible says for us to Love our enemies. I have used the wisdom from the Bible and it has worked. I hope it works for you.
Second, if that doesn't work... I'd put all the foreign poop in a bag and go next door and return it to them. Let them know that you know that it came from their yard because of evidence hanging in the tree, etc. Tell them that you don't know who is doing this, but that it is coming from their back yard. Ask them to please get whomever is doing this to stop this childish behavior. It might not be adults doing this. Remind them that you moved your children's playyard upon their request and that it isn't neighborly for them to be throwing poop over the fence. Let them know that you clean up your own dog's droppings and don't want your young children accidently getting soiled by the neighbor's dog's poop. Do they have teenagers? If so, it's probably not the adults who are doing this and they should be willing to take care of the problem by dealing with their teenagers. However, if they don't have teenagers, at least they will get the hint that you know were it's coming from and that you will not just ignore it. Let them know that you will take appropriate legal action if it continues.
Third, if 1 & 2 don't work, I would put a motion-activated surveilance camera facing the part of the fence where the poop is showing up and get it on camera. Make sure it is aimed so that you will be able to see who is doing it. Then, I'd send a certified letter, return-receipt-requested to them noting that you have them on film throwing their dog's poop over the fence and that if it happens again that you will call the police and file charges against them.
Hopefully, the first approach will work. Good luck.