Answer: No, this is expressly forbidden by canon law (Canon 874, §1). “To be admitted to undertake the office of sponsor, a person must:
1° be appointed by the candidate for baptism, or by the parents or whoever stands in their place, or failing these, by the parish priest or the minister; to be appointed the person must be suitable for this role and have the intention of fulfilling it;
2° be not less than sixteen years of age, unless a different age has been stipulated by the diocesan Bishop, or unless the parish priest or the minister considers that there is a just reason for an exception to be made;
3° be a catholic who has been confirmed and has received the blessed Eucharist, and who lives a life of faith, which befits the role to be undertaken;
4° not labor under a canonical penalty, whether imposed or declared;
5° not be either the father or the mother of the person to be baptized.
§2 A baptized person who belongs to a non-Catholic ecclesial community may be admitted only in company with a catholic sponsor, and then simply as a witness to the baptism.
It is the duty of a sponsor or godparent to regard his spiritual children and his perpetual charges, and to instruct them in the obligations of the Christian life, especially when the parents neglect their duty. A conscientious non-Catholic could not fulfill this obligation.