Can you force a partner to add a fathers name to a birth certificate throught the Courts ?

The birth happened overseas and a population certificate was signed and witnessed by the local authority (South Cyprus) by/for BOTH parents - not married - therefore parentage is not in question and the issuing authority has agreed to correct subject to affadavit - but one partner has declined to complete the required affadavit to effect the correction. The reason given by the partner is that they do not want the other partner on the certificate or in the childs life....which at best are questionable reasons.