I would say that you could buy a 3pt "Carry All" and a mount a water tank to it. Both are available at places like TSC or Northern Tool.
The water tanks typically come in 25, 35, 50 gallon sizes and larger. But unless you have a pretty large tractor you will have to be mindful of the weight. Water weighs about 8 pounds per gallon. I would probably start looking at the 50 gallon sizes and see if I could get an even larger one that would still be able to be carried. Most of the "Carry All" units have pretty limited weight capacities, as the gallons go up, you might find the need for a heavier duty carry all. I've seen some that will hold 1000#. That might make the front end of your tractor very light and hard to steer.
Most of the tanks I've seen have a drain on the bottom, you could probably remove the drain plug and hook a hose to that outlet. As long as the end of the hose is above the water level, the water will not drain out of the tank. You could simple let the hose down and gravity will drain as much of the tank as you need, then move on to the next tree.
If you want to get fancy about it, you could get a 12 volt pump and power pump water through a hose, that would allow you to drive up to the tree, flip a switch, shoot the water at the tree trunk and then move on, all without getting out of the tractor seat. I think you can get small pumps that will move a couple gallons a minute, but some of that flow depends on the spray head you use, if you even need a spray head.