Have you heard of the sapodilla tree (Manilkara zapota)?
This tree is native to Mexico and Central America, preferring zones 10B-11. While it can grow in the southeastern and southwestern US, check with your extension office before planting. It is considered at category one invasive in Southern and Central Florida. The official definition for Category one invasive species in Florida, as defines by the UF/IFAS enter for Aquatic and Invasive Plant is “Invasive exotics that are altering native plant communities by displacing native species, changing community structures or ecological functions, or hybridizing with natives.”
If safe for your area, this 60-100 foot tall evergreen tree produces a sweet fruit which matures from May-September.