I have an (old) German made 2-wheel bandsaw, which had what seemed to be hard plastic or nylon tyres. They were also breaking away, and where I live, there was no chance of easily shopping for replacement parts. After lots of experiments, I eventually ended up with tyres glued in place, made from hard leather. I thought this would be only a short term solution for the immediate job in hand, expecting the slight offset on the blade teeth to simply rip the leather up. However, they have now been in fairly heavy use for about a year, (Been building a sailing dinghy with it) and although showing signs of 'cutting up', they are still 'good to go' for a while yet (and I have half a cowhide to replace them when they do!
).
The original tyres did have a slight 'dome', and I had no way to replicate this with the leather tyres, but they work anyway, so I agree with Chris about that. I suspect the blade is sinking into the leather slightly, so they are acting a bit like pulleys with rims. It was cheap – I picked up the hide for next to nothing on our local market, and used impact adhesive to secure it.