In some countries a godfather or godmother is regarded by most people simply as a good friend of the family who sends gifts to the child annually. If that were all, there would, of course, be no objection to a Bahá’í accepting to be a godfather or godmother. However, even in such countries it is likely that, beyond assuming this responsibility, the godparent would have to take part in the baptismal ceremony of the infant and, although many nominal Christians may treat such matters very lightly, a Bahá’í should be aware of the solemnity with which the church regards the rite and should not assume an undertaking which he cannot fulfil or do anything which would imply a denial of his faith.
(Universal House of Justice, Lights of Guidance, p. 143)

In the case of non-Bahá’ís who are godparents of Bahá’í children, the changed obligations of their roles may be quietly discussed with them by the Bahá’í parents, who would point out that they may now wish to be freed of their commitments, and that in any case the religious aspects of the relationship are no longer in effect.
(Universal House of Justice, Lights of Guidance, p. 143)

The House of Justice has noted your strong emphasis upon the social and economic aspects of co-parenthood in your country, and your mention of the religious basis for the custom. While the diminution of Christian fervor among the rank and file of Dominicans may be great, nevertheless the baptismal origin and other religious aspects of godparenthood cannot be minimized, particularly for rural people who may well be under pressure from parish priests. Your Assembly understands that a conscientious Bahá’í couple must not have their children baptized, nor should Bahá’ís ordinarily participate as godparents in a baptismal ceremony for this also may seem to imply their affiliation with the church.
(Universal House of Justice, Lights of Guidance, p. 143)

The position of ‘godparent’ varies considerably from country to country, and from one Christian denomination to another. In many cases it involves the godparent in participation a religious service as a member of the church in question, and in assumption of the obligation to bring the child up in the teachings of that church. It is clearly impossible for a Bahá’í to become a godparent in such circumstances. However, where individuals have undertaken vows as godparents prior to becoming Bahá’ís, the Faith does not require them to disavow their promise, but the new Bahá’í should inform the parents of his change in religion so that they may make a change in godparents if they so desire.
(Universal House of Justice, Lights of Guidance, p. 142)

You ask about those who have undertaken vows as godparents prior to becoming Bahá’ís. Trustworthiness is one of the great qualities which must characterize Bahá’ís, and the new believer therefore, far from repudiating any commitments entered into before becoming a Bahá’í, must be ever more conscientious in discharging them. However, there are certain actions which would violate Bahá’í principles and from which the believer must abstain. Others would be incompatible with his allegiance to the Faith, such as the promise made by a godparent to bring up the godchild in the teachings of the Catholic church. In such a case the new believer could suggest to the parents that because of his new understanding of Christianity they would probably prefer to cancel that part of the agreement, at the same time explaining his willingness to continue to discharge the social and economic functions of the godparenthood. The whole matter should be dealt with in a gentle and conciliatory manner, in the hope of retaining the friendship and trust of all concerned.
(Universal House of Justice, Lights of Guidance, p. 144)

You ask whether a Bahá’í may ‘become the godparent of the child of a non Bahá’í if he made it clear that he is a Bahá’í, cannot promise to bring up the child in the Catholic religion, is not affiliated with the Church...’. He may do so, for in such a case all concerned are informed of his beliefs. If called for, an agreement may be drawn up, through the local Assembly or a lawyers, which would define the social elements of the co-parental relationship while committing the religious ones.
(Universal House of Justice, Lights of Guidance, p. 143)