Ah yes, "chicken of the trees".
When we were in the Caribbean, we had some mighty tasty iguana soup. The tail meat is tough. I recommend using a pressure cooker.
The best iguana repellant I have seen was a trifoliate citrus hedge.
Metal trunk protectors that are a couple feet high work well, putting cages around your smaller trees, having a dog that loves to chase things, and planting a lot of milkweed also helps.
Glue traps work fairly well but are horribly inhumane, and you are left with having to kill the iguana up close and personal. Plus, if you have tenderhearted neighbors, glue traps can start nighborhood wars...
Carolyn