Looks like the Country Essentials album is a compilation/reissue album. Discogs albums date his recording to 1967 (Paper Birds), though it was performed first(?) by Judy Henske in 1963 on an album of the same name.

Joe, the questionable line is "And that old mule, he got to be a buddy of mine"

beachcomber, is this the song you were looking for? https://www.azlyrics.com/lyrics/tompaxton/myladysawildflyingdove.html

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Thanks, cnd. That makes perfect sense. Correction made. -Joe-