Q. 1. Is there a procedure as to how one quits as the godparent to a Catholic child?
A. 1. To the best of my knowledge, there is no written prcedure as to how one goes about quitting as the godparent of a child.
While this is the case, I frequently hear from parents of godchildren who's godparents are no longer in the child's life for a number of reasons. One popular reason is that the godparent has moved away to another city or country because of employment or marriage. Accordingly, it can be said that in such cases, most godparents abandon their spiritual obligations towards their godchild.
Then you have the situation where the parent of the godchild and the godparent no longer communicate with each other due to personal differences. Because of this, the godparent is prevented from fulfilling his responsibility. In such cases, the relationship between the godparent and the child ends there.
So officially, while there is no way to quit as a godparent, unofficially, there are practices that clearly indicate an end to one's obligation towards a godchild.