There are so many covers complaints that I had to write about this. First, I avoid any cover that has that strong leaching petrochemical smell, the smell that comes from fresh vinyl or neoprene covers. I only promote rebounder spring covers that do not off gas. The best cover is made of naugahyde, the same material used on professional boxing gloves. Rebounders back in the day used be made of cloth or leather, these get moldy from sweat and daily use. Naughahyde is the only one that can be left in the rain or in the hot sun without damaging it.
Note: the thicker the cover the less noise that can be heard from the springs. Also, if not getting the balance bar, I strongly recommend a spring cover, especially if buying a bungee rebounder. If someone is planning on doing exercise and sweating all over the rebounder, make sure you get one a cover that is easy to clean and take off.