The fruit looks right but, the leaves on the unknown tree are smooth on the edge and the seed is very round with no obvious seam. The pictures of the Prunus have serrated edges and a flatish pit. This tree is growing on the edge of a wetland, under taller trees and among the palmettos. It looks like it has been there a long time. The green, immature fruit, are more oval with a little tip at the bottom.

Stenocalyx dysentericus? or similar?

That might be it. It lacks the calyx and it was definitely not as easy to separate form the seed as the pictures make it look. I don't know how distinctive those traits are. I'll have to remember it's there so I can watch for flowers next year. That might help make a better ID.

It looks like hog plum or tallow wood (Ximenia americana). http://www.sharonsflorida.com/hog-plum.htm

Ximenia americana is edible, but some specimens taste better than others. It also contains hydrocyanic acid so shouldn't be eaten in large amounts.

I like Ximenia as an option. I always forget about that genus!

That looks like it, right down to the thorns! Thank you all, for your kind help.

Fantastic!

Looks like Kei apple, Dovalis caffra.

I have plenty of this shrub and I would like to know the name and its characteristics. Thanks.

Did you read any of the comments? It was ID'd as Ximenia americana, aka hog plum.

We found some too and they are delish. you want to eat them when they are soft. it is like a citrus plum, tastes like a plum and orange together.

These make the most divine jam! Worth the time and effort. I used the directions for plum jam on the directions that came with Jell Well pectin but any pectin will work.