The short answer 

Everyone born in South Africa has the right to a birth certificate. You should be able to get a copy from Home Affairs. 

The whole question

How can I get a copy of my child's lost birth certificate? He was born in South Africa, but both his mother and I are Congolese. 

The long answer

The Home Affairs website says: “Undocumented Foreign Nationals who are born in South Africa are issued with a certificate free of charge on registration of their births.”

The Scalabrini Centre of Cape Town says that children born to two non-South Africans and who do not qualify for citizenship are entitled to a birth certificate according to the Births and Deaths Registration Act. But in those cases, children are given birth certificates that do not include an ID number and the child is not entered into the National Population Register.

Home Affairs must have a copy of the birth certificate, and you would have to fill in form B1—154 and submit it to Home Affairs to get a copy. That is the form that South Africans must complete to get a replacement birth certificate and I could not find any different instructions for foreign parents whose child was born here. 

It could take six to eight weeks to replace the birth certificate and the application fee is R75.00.

If you encounter difficulty at Home Affairs in getting the birth certificate, you could ask one of the following organisations for assistance: