They sound like a type of muskmelon. Especially, maybe, one of the apple-melon/dudaim types.

But if not...

Do you know if they were on vines, bushes, or trees?

How large were they?

How about their shape?

Smooth, bumpy, spined, or furry?

Any idea what they looked like inside?

Woops, I guess I could have posted a little more info.
That looks a LOT like it Brandon.

These were small, about the size of a peach and had skin like a plum....I think. Smooth textured on the outside. We never did try to cut them open.

All of this time I kept thinking they were called pomegranites but that doesn't match up.

And he always had them picked before we got there so I don't know what kind of plant they came on.

The dudaim muskmelons go by many "common" names including Vine Pomegranate, Apple-melon, Queen AnneÂs Pocket Melon, and Plum Granny.

Oh, they also smell very good (like you described). The common name, Queen Anne's Pocket Melon, came about because in pre-deodorant days, they were carried in people's pockets to help cover up BO. Lovely thought, huh (-: