How can I get a court order to establish paternity, when the father agrees that he is the father?

If the name of the father is on the birth certificate you may not need a court order. If both parents agree on who the biological father is, you can sign a statement called an Acknowledgment of Paternity. These forms are available at all birthing hospitals, the Office of Vital Records, the Division of Child Support Services at the Arizona Department of Economic Security offices, and many of the offices of the county registrar.

You may also establish court ordered paternity by completing paperwork and filing it with the court. A court order to change a birth certificate must have the birthday of the child on it. If you have a court order for paternity, the order may be filed with the Office of Vital Records directly by the court, the agency that petitioned the court for the order, or one of the parents may deliver it in person. If you decide to bring a court order to the Office of Vital Records in person, you must bring a certified copy of the court order with you. 
 
Resources:

Paternity information and court forms

Arizona Department of Health Services Vital Records – Corrections & Amendments to Birth Certificates

Division of Child Support Services – Voluntary Paternity Program