A similar version to "Devilish Mary" in the DT (the London-Londonderry version) was collected in Arkansas, 1930, with the chorus-
It's tararinktum, tararinktum, tararinktum ready.
Vance Randolph, Ozark Folksongs, volume 3, no. 437, pp. 186-190.
Randolph notes a version sung in Texas in 1897.

"Edna Ferber, in her novel Cimarron.... prints part of another version, as sung by Oklahoma cowpunchers in the 80's."

Randolph collected a version, sung in MO ("1900") in 1941, with a verse:

The first pretty girl that I came across,
It's dear oh won't you have me,
Hair all curled and a-wavin' back,
And they called her devilish Mary!

From another version, coll. in Arkansas-

Oh she tried to break my neck with the broom,
And fill my side with stitches,
She popped her fist right into my face
And swore she'd wear the britches.

She tried to break my head with the broom
And called me the very devil,
She said if I said three words to her
She'd bust my head with the shovel.
Cho.-
To my rye, rye, rye,
To my row, row, row,
To my rock and rye oh dandy!

Another chorus, from Mo:

Try de ma rink dink toddy rinka day,
Try de ma rink dink derry,
Try de ma rink dink toddy rinka day,
Called her devilish Mary.