Just noticed something interesting about this song. The Trinidadian version seems to be more explicit than the Jamaican ones. According to Gibb Sahib's post, "most mento songs are bawdy". I have a songbook, "Mango Time:Folk Songs of Jamaica". This song is on page 38 under the title "Hol'Im Joe".

Note: The only comment on the origin of this piece is that it is "A song about an unusual donkey".