I have a similar situation with my pond.
If you're willing to live with whatever kinds of fish are in the upstream pond you could build your pond to catch the spillway discharge from the neighbor. I didn't want the neighbor fish getting into my pond so I terraced and graded to take the upstream pond overflow around my pond.
There was a bit of erosion that happened before I got grass established on the back of my pond dam, but not to the extent that would be considered major damage. Without knowing the size of watershed you have it's impossible to say how much flow to expect.
