It seems that the most viable option would be a couple of trees, benches and individual plaques mounted either on the fence (the most space available) or on the back of the bulletin board. Although I will probably never (well, it IS unlikely) see the park, I think this makes the most sense. Especially if all plaques are the same size. I'm sure there are places that can make weatherproof plaques. Metal would last quite a while as would the composite decking material.

The composite could be cut into squares and the information for each pet branded into it, and a frame around the edges. Inexpensive, long lasting, uniform size. I'm sure there are some woodburners who could do it.