I would think the two most important factors are your
local rainfall and topography. If you make up a topographic map for your site and study it, you will see the natural locations for putting a catchment. Maybe just a half-circle a little downhill from your trees and pack some clay and organic matter as absorbent material will be
enough. It really depends on your rainfall. If you know the optimal rainfall for your trees, and yours is less than that, then you have an idea of how big the catchment will have to be to collect that amount of water. For instance, if you get 12" and your trees do best with 48", then you know that your catchment
should be about 4 times the area of the mature drip line circle of the tree.
If I get you right and you are going to do this at the single tree level, it sounds like something you could do with just a shovel in a few hours; build up a
berm downhill of your trees to slow and collect the natural rainfall. If you are more industrious, you could make an arced
hugelkultur mound at a radius from the tree and plant it with other plants you want in your food forest.
If you put a berm across the gully and end up making a (seasonal)
pond, then you will have to look into plants that can tolerate being flooded. And I will be glad to help you with that, because I'm giving away
bald cypress seeds.