Not sure you'll have success in fruiting a Medjool date palm here, though. They are a desert plant, probably not well suited to humid, wet Florida.
As far as coconuts go, there are coconut palms all over Siesta Key as street features, and in many other places in this area. They just are very diligent about removing the coconuts when they're getting big enough to fall. You never see one lying on the ground, unless it's in a private garden. It's not illegal to plant them, but you do have to maintain them.
