You don't need a big tree, build a frame yourself as described here: http://www.ehow.com/how_2146738_build-aframe-porch-swing.htmlIt's recommended that you get swing set plans instead of trying to design your shed yourself. Here is a good set of links to swing set plans:http://aboutswingsets.com/swing-set-plans/
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I'd recommend good old-fashioned wood. Do a google search for "swingset plans" or something similar - you should find a few free plans.
build the frame from thick metallic rails or water pipes
bolts are better than welding. if you use pipes you can use pipe connectors
add X bands where needed to prevent the construction from wobbling and breaking