Although Michael responded I thought I'd throw this out there.
Here in California there are manzanita shrubs everywhere seemingly. I'm not done with mine but you can make a parrot play tree out of any parrot safe wood by cutting a large branch off and then cutting it up the way you like. Of course wash and dry the branches in the sun and then continue on. Arrange the branches creatively. I tied mine with rope to see how I wanted it to look and then did the final step.
I've taken the lazy way and used stainless steel screws to screw them together, but you could use dowels to connect the branches so that it's all internal and therefore no metal would be exposed. It just takes some creativity, know-how and patience. Depending on your knowledge, willingness to research, and time you have to spend, you could definitely make a tree like Michael's or maybe something a lot less fancy, as with my case. :] You can do it! Here's a very rough guide:
http://www.ehow.com/how_6314249_instruc ... stand.html which is similar to what I did. I just winged it, hence the lack of beautification.