I wouldn't use any regular glue, and appologies to the person who mentioned gorilla glue, but that would be a disaster. It is a rather weak bond, isn't very flexible, requires moisture, and expands like crazy as it cures.
I've never glued neoprene to china
, but I've done lots of neoprene work in the dive industry. The best thing for neoprene is the neoprene specific cement. It off-gasses something knarly so definitely outdoor use only until cured. And it sticks to everything, so be tidy (learn from my mistake: be sure to put the lid back on tight.)
My preferred method is to outline the neoprene piece with chalk (you may have to use ink on china), then coat the neoprene and whatever you're attaching it to (stay inside the lines, again trust me on this one...). Let it quick-set, then stick the two together. Press firmly, but not so hard that you squish glue out the seam. Work the piece down flat like you were hanging a piece of wallpaper. The neoprene cement will remain pliable for its life, so I normally seal the edges with a bead of Aquaseal to reduce the potential for lifting.
If you can't get neoprene cement, I would second rubber contact cement. I've never used it with neoprene, but it seems the most similar to neoprene cement.
If it isn't too late to return the neoprene you've purchased, you can get an old used wetsuit from just about any dive shop for free or almost free. Just ask for a thrashed rental suit and cut out the shapes you need.