Since the date on the sheet music was 1853, I thought that date would be the definitive origin, but apparently not. I found the same song in 2 books, both dated 1847:

Songs of Ireland and Other Lands (New York: D. & J. Sadlier & Co., 1847), page 139.

The Granite Songster: Comprising the Songs of the Hutchinson Family by Asa Burnham Hutchinson (Boston: A. B. Hutchinson, 1847), page 49.

The first book does credit "J. Sinclair" however.