It seems that not a week goes by that we at Catholic Answers do not hear from parents who are having second thoughts about the appropriateness of a godparent of one of their children. See if you can pick out a common thread in these tales of woe:
Have you noticed that in each and every case the parent chose someone to be a godparent based on the closeness of the relationship rather than on the strength of the candidate's character or the maturity of the candidate's Catholic Faith? In all of these cases, the parent preferred a friend or relative to a mature Catholic.
To be admitted to undertake the office of [baptismal] sponsor, a person must: . . . be a Catholic who has been confirmed and has received the Blessed Eucharist, and who lives a life of faith which befits the role to be undertaken (canon 874, Code of Canon Law).
Because the godparent is an official witness to the baptism of the child, it is not an office for which a "replacement" can be made. It is not possible to go back and "redo" the sacrament of baptism, substituting in new and improved godparents. Once a choice is made, parents are stuck with that choice. For better or for worse, in sickness and in health, until death do you part.
That is why parents must take more care in choosing godparents. If your favorite relative or your Best Friend Forever or the person your family says "deserves" the job happens to be a mature Catholic committed to his faith and to the Church, then that person is a fine choice for your child's godparent. But if that person is a risky choice, either because of how he lives his life or how he practices his faith, then he is not a good choice. It is far better to stand up to pressure from family and friends now and refuse to make a risky selection for godparent than to wonder what you're going to do about a flaky godparent later.
Is there anything you can do about a godparent you trusted who turns out to not be all you hoped for in a godparent? It depends on the circumstances.
If it is a personality clash or a strained relationship, the best solution would be to do your best to mend fences for the sake of the child. Unfortunately, we live in a society in which no-fault divorce is applied not just to the sacred bonds of marriage but also to other sacred bonds, and people seem to have no problem declaring others "toxic" and distancing themselves rather than go to the hard work of repairing relationships. If you do your best on your end to fix a relationship, you are not responsible for someone else's refusal to uphold his or her end of the relationship.
If the godparent has fallen away from the Faith or fallen away from living a moral life, it may not be in the child's best interests to have that person involved in the child's religious training. You cannot replace the godparent, but you could ask another Catholic whose spiritual maturity and moral character you trust to act as a religious mentor to your child. Although canon law states that the godparent is the desired person to be the child's confirmation sponsor (canon 893), another person can be asked to be confirmation sponsor if the godparent no longer meets the requirements for the role.
The godparent relationship is not a one-way street, in which godparents are expected to provide emotional support, spiritual mentorship, and tangible goodies (such as money and gifts) while the children are but receptacles of bounty. Negligent godparents who fail to fork over the goods cannot be stripped of their godparenthood and replaced. Godparents do have responsibilities to their godchildren, and deliberate negligence and absenteeism cannot be excused, but godchildren are expected to participate in the relationship by offering their love, prayers, and sacrifices for the sake of their godparents.
In cases where godparents seem not to be living up to the responsibilities they agreed to undertake, perhaps their godchildren ought to be encouraged to offer their prayers and spiritual sacrifices for their godparent. Who knows? Maybe God can use the merits of a godchild's spiritual offerings to help a negligent or wayward godparent get his or her life back in order.