You could build up the soil on the downhill side to make some sort of a catch basin. Alternatively you could water on the uphill side with a drip emitter that would go into the soil with less runoff.

I am using bottomless coffey cans pushed about 1 to 2 inches in the soil and i fill them with water. the cans hold the water in place so it can go into the soil and spread. you can use a root feed on the hose end. I have a series of pits to pour water in and from their it spread. A misting device on a hose end could run for hours and not run off

All good ideas and inexpensive. Another thing you can do is amend the soil around the tree with gypsum to improve uptake of water.