In the Directory for the Application of Principles and Norms on Ecumenism, the Church says:
- It is the Catholic understanding that godparents, in a liturgical and canonical sense, should themselves be members of the Church or ecclesial Community in which the baptism is being celebrated. They do not merely undertake a responsibility for the Christian education of the person being baptized (or confirmed) as a relation or friend; they are also there as representatives of a community of faith, standing as guarantees of the candidate’s faith and desire for ecclesial communion.
a) However, based on the common baptism and because of ties of blood or friendship, a baptized person who belongs to another ecclesial Community may be admitted as a witness to the baptism, but only together with a Catholic godparent. 107 A Catholic may do the same for a person being baptized in another ecclesial Community.
b) Because of the close communion between the Catholic Church and the Eastern Orthodox Churches, it is permissible for a just cause for an Eastern faithful to act as godparent; together with a Catholic godparent, at the baptism of a Catholic infant or adult, so long as there is provision for the Catholic education of the person being baptized, and it is clear that the godparent is a suitable one.
A Catholic is not forbidden to stand as godparent in an Eastern Orthodox Church, if he/she is so invited. In this case, the duty of providing for the Christian education binds in the first place the godparent who belongs to the Church in which the child is baptized.
The Church only mentions the Eastern Orthodox in this document, as for standing in for other denominations, i think you need to receive counsel for each ecclesial community as some might not practice valid baptism (In the Catholic Church’s view). So you might need to ask your Parish Priest (pastor) for advise on the particular church a potential godchild is being baptized.