The core of the Church’s regulations on godparents are here:
10. Therefore godparents, chosen by the catechumens or by the families of children to be baptized, must, in the judgment of the parish priest (pastor), be qualified to carry out the proper liturgical functions mentioned in no.9.
It might seem curious that the Church expects catechumens to choose their own godparents, but it would seem that an adult would be a good judge of character and example, more or less. The pastor has veto power, as it were.
1. Godparents are persons, other than the parents of candidates, who are designated by the cnadidates themselves or by a candidate’s parents, or whoever stands in the place of parents, or, in the absence of these, by the parish priest (pastor) or minister of baptism. Each candidate may have either a godmother or a godfather or both a godmother and a godfather.
This guideline is taken literally. I’ve known two instances in which the parents of a child requested two godmothers. In neither case was the suggested pair a same-sex couple–the family simply had two close women friends who were thought to be good examples. If memory serves, in one case, the second woman was listed as a “Christian witness.”
2. Those designated must have the capability and intention of carrying out the responsibility of a godparent and be mature enough to do so. A person sixteen years of age is presumed to have the requisite maturity, but the diocesan bishop may have stipulated another age or the parish priest (pastor) or the minister may decide that there is a legitimate reason for allowing an exception.
The bishop determines the age, but in effect, a pastor can, for good reason, make an exception. More than once I’ve seen a significant other requested by the catechumen. That’s a touchy situation that’s sometimes, but not often, a positive experience.
3. Those designated as godparents must have received the three sacraments of initiation, baptism, confirmation, and eucharist, and be living a life consistent with faith and with the responsibility of a godparent.
4. Those designated as godparents must also be members of the Catholic Church and be canonically free to carry out this office. At the request of parents, a baptized and believing Christian not belinging to the Catholic Church may act as a Christian witness along with a Catholic godparent. (canon law 873-874) In the case of separated Eastern Christians with whom we do not have full communion, the special discipline for the Eastern Churches is to be respected.
I’m assuming the special discipline for Eastern Christians is not a serious obstacle, in that we would recognize a valid confirmation and eucharist in said churches.