Visa for South Africans

A Special Pass may not apply to you, as its usually issued to those doing things like volunteer work, temporary work, waiting for work permits and so on.  If you are a tourist, its not the correct visa.  It also costs Ksh 15,000 per month.  Considerably more than a 90 day entry permit.

However, you should be able to apply for a 90 day extension.  For those of us who enter Kenya with a visa have the right to make one in-country application to extend it by 90 days.

As above, you do this, in person at Nyayo House.  Take some passport photos with you (there is no photo booth at Nyayo House) and a I seem to remember that passport photos are needed.