You surely have the right to do so. You were chosen to be a steward of faith for the girl, to serve as an added assurance (in addition to her parents) that she would be raised to fully understand her relationship to God and to Jesus and to have a life in the church. A good godparent is not just fulfilling a social role; presumably, you weren't chosen because you were only a good relative or the girl's mother's best friend. There had to be other qualities in you that inspired your selection.
A good godparent might pray for her godchild every day; give the child special, hopefully spiritually oriented gifts on her birthday or on the anniversary of her baptism; and make sure the child attends Sunday school and has an age-appropriate Bible. Some godparents even regularly pray with their godchildren. All this suggests the enormity of the duties you agreed to take on when you became a godparent. So you certainly have the right to discuss your concerns with your goddaughter's parents. But don't forget: As the girl's parents, they make the final decisions about her upbringing. You can attempt to influence them, but you have little recourse if they ignore you.
Q. I'm not a Christian and was wondering how the godparent tradition started.
The responsibilities now borne by godparents began in the fourth century when the Christian Church, under persecution from Roman authorities, was concerned about being infiltrated by pagans. A person who wished to be admitted to the church had to have sponsors who would attest to his faith as well as assist him in preparing for these initiatory sacraments and in later living a Christian life. About the year 800, when infant baptism was the norm, sponsors would take the Profession of Faith in the child's name, as well as agree to instruct the child in the faith if his parents failed to do this. Such a sponsor was called patrinus, or "godfather."
Quite possibly, the idea of this witness who confirmed the intentions of someone converting to Christianity was borrowed from Judaism. At a baptism, or mikvah, for a convert, witnesses would vouch for the candidate, who was then baptized in water, after having been circumcised if a male.
Q. Catholic friends want me to be the godfather to their son. But I'm Presbyterian. Can I be a godfather to a child from a different denomination?
Your own church would have no problem if you became a godparent to a child from another Christian denomination, or if you asked a non-Presbyterian Christian to be your child's godparent. The Presbyterian Church only asks that a godparent believe in Jesus. However, the Vatican insists that a godparent to a Catholic child be a Catholic who has received the sacraments of Holy Eucharist and confirmation. Canon law also states that a godparent "lead a life in harmony with the faith and the role to be undertaken." Catholics who do not regularly attend Mass or are in marriages that the church considers invalid must disqualify themselves as potential godparents. (An invalid marriage is one in which a partner's previous marriage has not been annulled.) The church's reasoning for precluding such Catholics from being godparents is that someone not fulfilling his or her own religious obligations will not responsibly help another person do this, which, of course, is a godparent's essential task.
But Catholicism does let a faithful Protestant or Orthodox Christian be a "Christian witness" to the baptism. This is as close to being a godparent for a Catholic child as a non-Catholic Christian can get. The reason for this distinction is that godparents explicitly promise to help raise the child as a Catholic, and a Christian who is not a Catholic cannot fully attest to the beliefs of the Catholic Church. (Conversely, the Vatican has ruled that a Catholic can only be a "Christian witness"--not a godparent--for someone being baptized into another Christian denomination.)
Q. For my nephew's circumcision, I've been asked to be the sandak, the person who holds the infant during the circumcision. But I hear that a sandak is the Jewish equivalent of a godparent. If so, I don't want to hold the boy at the bris because I don't want the religious responsibilities that'll come later in life. How do I get out of this?
Don't worry. The honor of being a sandak has nothing to do with being responsible for the boy's future religious or moral education, which is the Christian idea of a "godparent." In Judaism, there are no godparents; unlike Christianity, Judaism reserves exclusively for biological parents the responsibility for their child's religious upbringing.
Traditionally, being a sandak is a meritorious religious act; to the kabbalists, it even had qualities of atonement, perhaps because a sandak is the person who is physically presenting the child into the Jews' covenant with God, which extends in an unbroken line to the patriarch Abraham, who painfully self-circumcised himself when he was 99 years old.
Among some Sephardic communities, the sandak customarily buys clothing, blankets, and diapers for the baby. And in many Jewish communities, it's the custom for a grandfather to be the sandak, while the grandmother, who hands the child to him, is called the sandakit. There are other names for the sandak: tofes ha-yeled, "holder of the child"; av sheni, "second father"; and shali'ah, "messenger." Jews of European origin may use the term kvater, a corrupted form of the German word gevatter, which means "godfather," but not in the Christian sense.