To me it sound like you want drip irrigation. You can get hose with inbuilt drip emitters or you can mount the emitters to hose which has no emitters. The emitters give a predefined amount of water per hour and you can make circles or other shapes with the hose and associated components

The problem is that drip irrigation that has to be hooked up to a hose could be too slow when you have a multi-tree situation and have to drag the house out, wait 5 hours, drag it to the next tree, wait 3-5 hours, etc, etc, etc...unless it's something you can "fill and forget" that would then drip out.

Treegators are one idea, but they don't seem to distribute the water that well, since they only have 2 holes.

Right now this isn't something I am doing, but I'm envisioning something I'd like to do, and it involves about 12 trees. I don't have the time to drag a hose to 12 trees, hooking them up, waiting 3 hours, then moving to the next onem, especially at the beginning when they need a lot of water at transplanting.

What about 5 gal. buckets and small diameter hose available from hardware store? If you want 10 gal. use 2 buckets and several siphon hoses to distribute the water evenly. The more buckets and hose the more trees you could water at the same time.

Lee Valley Tools has a couple of systems that might be just what you need. I plan to use one myself.

I can't put two links below so here is a pastable link to one of them and the other is below: http://www.leevalley.com/en/garden/page.aspx?p=59394&cat=2,2280,54307

Here is a link that might be useful: Tree irrigator