Most religions suggest that anyone in a Godparent/Sponsor role should be close to the family, either as a member or a very dear friend. There's also usually a "practicing" clause: before I could become my niece's godmother, I had to present a written acknowledgement that I was a practicing Catholic. It's a sacrament, so it's not supposed to be taken lightly.
I don't get the feeling that your family has a really close relationship with the coach outside of skating. That's a tenuous situation: one move, marriage/divorce or coaching change and that link of being a sponsor is broken.
I know several couples whose close friends (at the time) were chosen as Baptismal godparents for children; in one case, they were godparents to each others' children. Unfortunately, only a few are still close friends; most no longer see each other and are now strangers to the children. ActuTsame is true of my twins' godparents, who were married couples. One set of godparents are divorced now. The second godfather passed away unexpectedly and his widow converted to another denomination. She's engaged to be married next year, which is wonderful for their new family. (DH is her daughter's godfather.)
We're still friendly with all of the surviving godparents, but we see our oldest DD's godparents far more often since they're my sister and BIL. That's the main advantage of asking a family member - most people stay in contact with family, even if they don't like each other, lol.
On the other hand, my late MIL's best friend was in her wedding party, became DH's Godmother, "stood up" for him at Confirmation, and witnessed our wedding certificate. She's still part of our lives at 90+ years of age - in fact, DH is visiting her this weekend.