"The Marigold" is certainly a close relative, with a similar shape and tonality, but it isn't quite "The Star."

An early melody virtually identical to "The Star" may exist somewhere under another title, but there are so many relatives around that it seems pointless to search for a precise match. It could easily have evolved without notice.

We don't even know if McGarvey set the tune himself: someone else may have turned McGarvey's verses into a song.