This waltz has been given a different title on every recording it was featured on - on "Sligo Ceili" Seamus Tansey called it Michael Coleman’s, which is the title I’ve always used, although I don’t have that rarer-than-rare LP myself (!), I think I came across it in a book (probably the Fiddlecase publications tunebook); on some pressings (!) of Joe Ryan and Eddie Clarke’s Crossroads LP it’s called "Kevin’s Viennese," but on mine and in the database here it’s simply titled "Old Time Waltz." On a late 60s LP from the Connaught Ceili Band it’s "Joe Connolly’s Favourite." On the Spirit of West Clare Bobby Casey didn’t have a title for it at all.
One fellow on IRTRAD-L theorized that the Kevin mentioned above was box player Kevin Keegan, who played in the Aughrim Slopes Ceili Band; he succeeded Joe Mills in that role, who is said to have liked this tune a great deal, and had yet another title - the Diablo Waltz. There are a few tunes out there on old sheet music with that title as well so perhaps it’s an old ballroom tune of some sort?
Connaught Ceili Band recording download: http://www.capeirish.com/tune_vault/#ccb
IRTRAD-L discussion: https://listserv.heanet.ie/cgi-bin/wa?A2=ind0202&L=irtrad-l&D=0&P=56539