Thats extremely strange. I changed my childs surname to mine (same situation as yourself), no problem. Filled in forms and paid R50. The signature of the biological father was not necessary as my child was born out of wedlock. This was about 6 years ago but it seems that the system has changed (see below).
A parent may apply to change surnames of a minor if the child was born out of wedlock and:
•the mother married someone else other than the natural father of the child
•the mother remarries someone other than the child's natural father.
•the child's mother resumes the use of a surname previously used, the child's father has passed away or the mother remarried after divorce
•if the names were registered under the natural father's name. The child's surname can be changed to that of the mother.
Steps to follow
•Complete application form BI-193 at any Home Affairs office. Apply at a South African embassy or mission if you are abroad.
•Submit copies of :
◦marriage certificate if legally married except in the case of guardianship
◦decree of divorce and death certificate of natural father except in the case of guardianship.
◦proof of guardianship and
◦a written consent:
■from the person whose surname the child is assuming
■from both parents as well as sufficient reasons, in writing for the change (where applicable)
■from the natural father unless waived by a competent court.