Legal Question in Family Law in California

It cannot legally be done. The problem is that termination of parental rights terminates parental responsibilities. The law will not allow you to deny your child the duties owed by parents to children unless you are declared totally unfit as a parent, and since you are divorced and the child can live with the other parent, even that probably would not do it. The only other option is if someone is willing to take on your duties along with your rights by adopting the child, such as if your ex remarried and he and his new wife did a step-parent adoption. Other than that you can do whatever informal arrangement you want with your ex, but the courts will not give it legal effect.