Sailrite is a company in the US known for kits to make sails and other boat-related projects. They sell trampoline mesh -- in black only I think.

Sail Rite Mesh

Not sure what kind of PVC-coated material you would use for edging, as I haven't researched that much yet. Was thinking about making a mesh tramp for one of my boats. I have a home-use machine, but it's a high-end one (Bernina if you're interested), and I've done all kinds of canvas work, tramp repair, etc. I just made a snorkel so I could leave the jib on my Hobie 18 up on the boat. I don't expect to have any problems when I go to make the trampoline. I already have a grommet kit, and it's very easy to use.

If you were looking for a first-time project, I can't think of anything much easier than a tramp -- basically two squares of material (3 if you want to do old-style), with edging sewn all around. Then you add the grommets, and any pockets, and you're done.

Go for it!
Shambie