It's true that Child didn't include many tunes. This was because he didn't know that many of these songs HAD surviving tunes; he worked from manuscript, not oral tradition. The collection to look at for tunes is Bertrand Bronson's The Traditional Tunes of the Child Ballads.

Having said that, most people who sing these songs do sometimes write or adapt tunes, and many use tunes written by previous folksingers. Few listeners would object.