If the father is willing to cooperate, you can submit a completed Acknowledgment of Paternity form to the Oklahoma Department of Health Vital Records Service. After they accept the form, they will amend the birth certificate to include the acknowledged father. You can get the form from the Department of Health, or any hospital with a maternity ward.
If the father does not wish to cooperate, you can file a Petition with the district court to determine parentage. If the father admits paternity or a DNA test determines paternity, you can get a court order declaring him the father. You can then use the court order to amend the birth certificate.
If we do not have a written attorney-client agreement: I am not your lawyer; you are not my client; this is not legal advice.