I am a lawyer, and work in the Children's Court quite often. In terms of the Childrens Act (Act 38 of 2005) you can only be appointed as a
guardian of a child by the High Court. So the only way would be to get a lawyer to do such an application, although I can't see that the Court will grant guardianship to you, since the biological parent is still alive and able to maintain the child. A High Court application can also be very costly, even if it is unopposed.
Another option might be to
adopt the child, the mother will have to give permission for that, as well as the biological father of the child, if he is still alive.
I think the suggestion made by 'Allo Allo' to get a medical aid for the mother and register the child as a beneficiary will be much better. Although i don't agree with the tone of the comment - (i think what you want to do is commendable and you really care about this child)- i think you also have to think about the psycological impact on both the mother and child. If i was the mother of a child that my boss wants to put on a medical aid, i wouldv'e felt like a failure, feeling that people think i don't take proper care of my child. The child will obviously also get older - and might possibly reach a stage where he/she will either resent his/her mother for not having a medical aid herself eg., or feel guilty that his/her mother doesn't have the same medical care.