In the state of Iowa what right does a father have if hes not on the birth certificate?

Unless paternity has been established by some method (for instance Child Support Recovery may have required a paternity test prior to requiring child support payments), the father may have no rights.  Paternity must be established, and this may require a Paternity lawsuit to establish rights. I would suggest contacting a local attorney to discuss this situation. A lawsuit would clearly establish the rights of the father including visitation and support.