I found a book called The History of John Wesley's Coat: Showing by Whom It Has Been Worn, and How It Has Been Trimmed [anonymous] (Derby: Richard Keene, 1851)

It seems to be a satirical, anti-Methodist pamphlet of 56 pages. The preface says it is patterned on Swift's Tale of a Tub. I don't know if there is any connection to the song.