Found this in a woman's digest magazine.
ADOPTION
A grandparent may adopt a grandchild if the parents' parental rights are terminated in a dependency proceeding, if the child's parents are deceased or if the parents consent. The adoption of a child is permanent. The child's biological parents no longer have any legal rights or responsibilities where the child is concerned. A court order is required. The adoptive parents may allow visitation between the child and the biological parents unless there is a court order prohibiting visitation. The biological parents are not required to pay child support to the adoptive parents, though they may be required to pay past due child support that was owed before the child was adopted. If the parents consent to the adoption or if the parents are deceased, this procedure can be completed in a few months. Grandparents, other relatives and persons who are not related to the child may be considered as prospective adoptive parents.
Since you mention joint custody then adoption is not what you want to do or even guardianship as you would have to terminate your parental rights through court.