I don't remember the exact name of what we used, but I know it's some sailboat rope. I think like 1/8". We never had any problems with it. It didn't stretch much either. If you have a local West Marine, that's where we bought ours from. I tried finding it on their website, but I didn't find it.
This is probably pretty close:
http://www.westmarine.com/webapp/wcs...$@#$@#$@# Num=11452
Our's is blue though, so it may be a different brand. Look at the breaking strength... 530lbs. That's a lot of trackballs.