I'm currently making a tramp as well. I went to our local sailmakers and picked up 2 metres of material for $50, (AUS), or thereabouts. The sewing machine I'm using is an old 40's electric Singer. It does only the one stitch, but it does it well.

A few things I've found:
Thread matters. I've chosen a strong nylon thread, as I figured it would cope better than cotton with the conditions. I was looking for a fine fishing line, but this is pretty much the same thing. I even found one in "smokey", so it is almost invisible on the tramp material.
The Singer is perfectly adequate to the task, but I did have some trouble getting the tension right. Once it was ok, I found that it has no problems, even through four layers of tramp material. The stitch is very strong, but I am triple-stitching everything for added strength.
I'm not using an edging material. This was traditional, but the edging seems to deteriorate faster than the tramp material itself, so I decided not to bother. I'm not sure yet if this is wise or not. As a result the edges won't be as strong as on some tramps, but I am making up for this with extra care in the stitching.
I spent some time with a soldering iron melting back the edges where I cut them, to prevent fraying. As a result I figured I can get away with just folding one edge over, rather than the two I would normally do with material. This keeps the overall thickness down, which helps with the sewing.
I still have two problems - I think it will be a tad thick where the rope is to slip into the holder on the hulls, but I will see about that later. Anyway, hard to fit is better than too thin. And I haven't found any eyes yet that I'm happy with for the rope to run through - I found some brass plated ones, but I'm hoping for something better.
Overall, it seems to be working ok, but it's a fair bit of work. The good bit is the $400+ I'm saving on the tramp can go into other equipment. btw, a while back I was a professional Teddy Bear Artist.

I would be more comfortable making the tramp if I could make it out of fur.
Have fun!