I just finished making myself a nice longbow out of blackolive, don't know if it grows in you all areas,but it does in south Florida ,It shoots very fast and smooth no vibrations, also cypress is used by the Osceola tribe and the Miccossukees.
We also have the sea grapes trees ,bends very well , you can hardly brake it ,even if you tried.
I do have an osage ,but unless you have good wood working equipment is hard to make bows, although a good sharo machete is your best tool to work it.

Have fun !