I remember singing this song in a Country school when I was kid.
But the first version recorded in 1928 by Anna and Julietta Canova.

Secondhandsongs.com says:

This song probably originated in Scotland circa 1600. Its first publication as words with an associated tune is dated to 1611 under the title “The Marriage of Frogge and the Mouse”. The song is known under many names, including, “Froggie Went A-Courting [or “A-Courtin’”]”, “The Frog Came to the Myl Dur”, “Frog in the Well”, “The Frog’s Wooing”, “The Frog and the Mouse” and “There Was a Puggie in a Well”

LYRICS
A frog went a-courtin’ and he did ride, M-hm, M-hm
A frog went a-courtin’ and he did ride
Sword and pistol by his side, M-hm, M-hm

The song may have originated as a satire of Queen Elizabeth’s habit of giving animal nicknames to her ministers. A version was created to express popular displeasure over her proposed marriage to a foreigner. Sir Walter Raleigh was known as her fish, Leicester her lap dog, and at the time of her proposed marriage to the Duke of Alencon and Anjou, Simier, the French ambassador was her ape; the Duke himself her frog. The song actually became something sung in nurseries and passed down that way over the generations.

The odd marriage party gets out of hand, with different outcomes to the participants in the various versions,
ranging from death to frog and mouse to living happily ever after.

SecondHandSongs lists 91 versions of the song,
but I’m sure there’s more. 

And I’m sure there’s a few ribald versions as well.