Many office supply/stationary stores will sell rubber bands large enough to do a similar job.
I've managed to find a large rubber band 200mm long and 12.5mm in width. It would be too wide to fit on a standard TECHNIC pulley, but you can attach it to any TECHNIC wheel rim wide enough such as 56145. The grooves on either side of the wheel rim should keep the band from slipping.
I don't know exactly what you plan to build, but you might want to also consider other ways of ways of transmitting power, could you perform the same function as efficiently using a drive shaft.