In California, the family court has no jurisdiction to terminate parental rights absent an agreement. Even if the court could, failure to pay child support is insufficient reason to terminate a parent's rights. Your only option is to get your ex to sign off on such a stipulation. If he agrees to sign off on his parental rights, I would highly suggest you hire an attorney to do the paperwork.
Step-parent adoptions are common, and they are not difficult to accomplish if the other parent agrees. Hire a family law lawyer in your area and get the adoption going before your ex changes his mind. It is true that the unpaid support is not a reason for a court to terminate parental rights. The fact that no further support will accrue, however, is good motiviation for a father like this to sign the adoprion papers and agree to give up his rights. Good Luck.
David C. Beyersdorf