Yes, new regulations came into effect in 2015 for people that travel to South Africa with a child.
In an effort to help stop child trafficking, the South African government implemented the rule that any adult entering or leaving South Africa with a child (under 18 years old), must produce the child’s birth certificate at the time of entry or departure.
If the child is not accompanied by both parents, a signed affidavit from the parents needs to be shown, giving the adult permission to travel with the child. If only one parent is traveling with the child, that parent will also need a signed affidavit from the non-traveling parent, giving permission to travel with the child.
Here is a PDF leaflet from Home Affairs that spells out all the rules.