New godparents cannot be chosen because they cannot serve as witnesses to a baptism they did not witness (which is part of the responsibilities of godparents). However, should a child’s godparents refuse their responsibility to assist the parents in educating the child in the faith, the parents can ask other Catholics whose orthodoxy and spiritual maturity they trust to be mentors to the child. (In other words, the parents can ask someone else to fulfill the role of assisting them in raising the child within the faith.) In time, the child may decide to ask such a mentor to become his confirmation sponsor.
Of course, should the original godparents wish to resume their responsibility and demonstrate that they now intend to honor their commitments, the parents may choose to invite them to assist in the child’s religious education.