I would call the church where the funeral was held and ask if they can help. It's very likely that there was a service bulletin listing the music; these are usually produced by the church's office staff. Their choir director might also be listed in the church's website, maybe even with an email link. A call like that would be a pretty routine thing for a church secretary to field. I know ours would be happy to find out (possibly sensitively would be needed), and get back to you; just mention how moved you were by the child's service. You don't need to be a member of that (or any) church to reach out.

~Susan