What pests attack seagrapes?

Answer 1

Seagrape borer:
http://creatures.ifas.ufl.edu/trees/moths/seagrape_borer.htm

Also:

"A nipple gall causes raised, red nipples on the upper leaf surface. "

http://edis.ifas.ufl.edu/ST175

Answer 2

Cocoloba uvifera is the botanical name for this tree. In its native environment it is quite resistant to pests, but it can become infested with a borer that attacks the ripe fruit. I used to harvest the fruit to use the seeds in propagation, and to protect against this I would wrap the fruit clusters in cheesecloth and periodically dust them with a powdered insecticide.