It may be that the tune as we know it today got its name from Gavan's song; or he may have taken his cue from a tune he knew. Whether it was set to an existing tune I haven't been able to discover, though naturally there are references to 'Rocky Road' tunes in various early C20 collections of Irish music. None of these, it appears, can confidently be said to pre-date the Gavan-Clifton song, except anecdotally.

The Fiddler's Companion has some useful information (including a report of the anecdote that Dave mentioned) but it assumes uncritically that the song must have been later than the tune and doesn't credit either Gavan or Clifton, so should be used with caution.