Well, surprisingly enough, John McCormack did not record it until 1929 as well. In fact, his studio recording is from 1930. I would certainly have been willing to bet that he recorded it before then.

This information is from the EXCELLENT John McCormack Home Page by Paul W. Worth.   Definitely worth a visit, plan on staying a while.

• Rose of Tralee, The (C. Mordaunt Spencer/Charles W. Glover; or words and music? by William Pembroke Mulchinock; or words & music are traditional)
  • film 35mm, 70mm (1929)
  • BVE 58586-1, -2 (19 February 1930)
  • Notes: References differ regarding the credits for this song. It seems possible that Spencer and Glover adapted a song for publication that they assumed was traditional. It may also be that Mulchinock wrote the lyric and fitted it to a traditional melody. The notes to Rego RCD-3022 cite an article in "The Kerryman" (newspaper), dated 7 December 1935 assert that the song hails from Co. Kerry and was written about 90 years earlier (ca. 1845), and that it was popular in Kerry for a long time. This article goes on to cite an anthology of Irish poetry, The Minstrel of Erin, published in 1903 (Fodhla Printing Co.), edited by Terence O"Hanlon, in which the verses are given as anonymous. In Mulchinock's obituary ("The Nation," 1846), the 1935 article continues, he is described as "a well-known contributor to "The Nation" and is given credit for writing "The Rose of Tralee." The Rego notes also cite a July 24, 1909 article in "The National Hibernian," Washington D.C. which credits Maurice Musgrave as the composer (presumably of words and music). Uncertainties about the origins of this song have yet to be clarified.