I've seen pawpaw and American persimmon growing along streams in floodplains, so I think they should do pretty well. Both are tap rooted, and I think are pretty drought tolerant once established.

Pretty much nothing.
I grow wild and domesticated berries, and everything I grow can't stand wet feet. Currants, blueberries, brambles, gooseberries, etc.
It's the standing water that is the problem. 18 inch raised beds might work for berries, but trees would probably still be too wet. Many trees grow in those conditions, but no fruit trees I know of. Use a lot of peat in the beds.
I have a few spots in my yard where water stands for maybe 10 days a year. I gave up long ago on growing anything in those spots. Well one I put a 12 inch raised bed, and it did work very well.

I can think of quite a few non-edibles that would grow there...red maple, baldcypress, etc...but nothing with edible fruit.

What about blueberries?

For every article that says blueberries can take wet feet, there's one that says they can't.

Hairmetal,

It's true traditional fruit trees like well drained locations. Nevertheless some fruit trees will tolerate a surprising amount of water once they're established.

From my experience apricot (on apricot roots) and peach (on peach roots) won't tolerate much water. Apricot will tolerate less than peach, but both need to be on well drained sites, or raised plantings, to perform well (or live).

Apple, plum, pear, and tart cherry (on Mazzard - not Mahleb) will tolerate some wet feet. My current thought is that apple on seedling roots is the most water tolerant of the bunch, with pear perhaps a close second.

Plums on myrobolan are pretty water tolerant but they are a little harder to get started (in general) and so water stress simply adds to the difficulty (I'm speaking of Euro plums. Japanese type plums are easier to establish).

That said, I wouldn't be afraid to put any of the more water tolerant fruits I mentioned in the spot you describe, if you could build even a little mound, as Drew mentioned, and planted shallow.

I've planted both persimmon and pawpaw in wet locations. Persimmon will take a lot of water, but pawpaws didn't do well in water saturated areas and I lost some. I agree with Alexander, pawpaws naturally grow near streams in the wild, but I think the difference is they are seedlings. Grafted pawpaw are much harder to establish.

I've found erect blackberries will tolerate loads of water (and drought as well) once they're established. They're tough.

One side effect of planting a somewhat water tolerant fruit tree in a wet spot is that vigor is greatly reduced for several years. The tree will not size up for long time. Consequently fruiting is generally delayed. Still if you want to plant a fruit tree in a wet spot, it will become productive if the tree doesn't drown before it gets established. It just takes longer.

Mounds, or some type of raised planting is the sure fire method to prevent drowning.

Pears and plums are both more tolerant than other common tree fruits and excess water doesn't seem to reduce plum brix.

I think pawpaws are naturally slow growing.

I've heard that some hawthorns can handle saturated soil as well as drought and are compatible with some varieties of pear.

Are there any trees currently doing well there?

"Mango" is a pretty fast growing pawpaw and excellent in eating.

I have seen wild pawpaws in two feet of water only a month or two before ripening. That flooding probably lasted for a week or so.

I also have established orchards on mounds in areas with nearly permanent surface water. Only problem is that most insecticides are illegal to use in such conditions. You can't spray without the poisons getting into the water system.

Mound up the dirt enough and most plants will grow much more vigorously than on the flat- a permanent source of water 2-3 feet below and the loose soil works very well. Blueberries maybe don't need as high a mound- they grow around here on hillocks in marsh but don't develop the kind of roots that drill far for water.

I have similar conditions and raised most things up. For the Cherries I made Cherry Hill and for pears and apples only small mounds. The blueberries that were planted at soil level died so I made Blueberry Island ect.. Many truckloads of soil. it's a shame cause the native soil is good sandy loam.

One other possibility is to add drainage tile to an area of your land, removing some of the water and lowering the water table. This of course presumes that you have some elevation to work with, and access to the machinery to put in the drain tiles or tubing.

I did this many years ago on my land back east, and it allowed me to plant apples and peaches in what was before a near swamp.