Some bike shops will hire mountain bikes - have a look at this question for a list of MTB shops in Joburg.

Alternatively you can hire a bike (R70 for 3 hours incl. helmet) and ride at Groenkloof Nature Reserve in Pretoria, there are some excellent trails for both beginners and experienced riders.

I know that Linden cycles specificaly will rent out bicycles. Its not going to be a "top of the Range" bike, for obvious reasons, none the less you will get a bike.

They work on a deposit system, where you will pay a deposit (which you get back when the bike is returned) and then pay a daily rental on the bike.

Good luck.