I'd just clean and sand the area on the stay where it goes and put some resin on it and let it cure. You might find someone familiar with CF and see if just regular Epoxy resin is okay or not.

Epoxy will be stronger than that rivet. So don't even bother with that. A hole in that part of the stay might not be a good thing. A little bit of glass or carbon fabric layered over the foot of that stop and onto the stay will further make it stronger. But that might be more than is needed.