"Peter, Peter, pumpkin-eater, / Had a wife and couldn’t keep her; / He put her in a pumpkin shell, / And there he kept her very well” is a traditional children’s rhyme from at least 1797.

“Cheater, cheater, pumpkin eater” is a modern “Cheater!” shout based on the rhyme. “Cheater, cheater, pumpkin eater” has been cited in print since at least 1992.


Wiktionary: cheater, cheater, pumpkin eater
Etymology
Based on a traditional children’s rhyme: “Peter, Peter, pumpkin-eater, / Had a wife and couldn’t keep her; / He put her in a pumpkin shell, / And there he kept her very well.”
Noun
cheater, cheater, pumpkin eater (plural not attested)
1. (childish) Someone who cheats.

Wikipedia: Peter Peter Pumpkin Eater
“Peter Peter Pumpkin Eater” is an English language nursery rhyme. It has a Roud Folk Song Index number of 13497.

Lyrics
Common modern versions include:

Peter, Peter pumpkin eater,
Had a wife but couldn’t keep her;
He put her in a pumpkin shell
And there he kept her still.

Peter, Peter pumpkin eater,
Had another and didn’t love her;
Peter learned to read and spell,
And then he loved her very well.

Origins
The first surviving version of the rhyme was published in Infant Institutes, part the first: or a Nurserical Essay on the Poetry, Lyric and Allegorical, of the Earliest Ages, &c., in London around 1797. It also appears in Mother Goose’s Quarto: or Melodies Complete, printed in Boston, Massachusetts around 1825.

(Oxford English Dictionary)
pumpkin-eater n.
1833 Mother Goose’s Melodies 67 Peter, Peter, pumpkin eater, Had a wife and couldn’t keep her.
2004 S. Selvadurai in Story-Wallah 363 You’re a cheater, cheater pumpkin-eater!

Newspapers.com
24 February 1992, Gaffney (SC) Ledger, “Modern conveniences, modern pains” by Janice Durham, pg. 4, col. 2:
“Now give me my Coke,” I rant. “Cheater, cheater, pumpkin eater.”

Google Groups: rec.humor.oracle
Usenet Oracularities Digest #450
oracle-...@iuvax.cs.indiana.edu
5/29/92
(...)
Realize that use of the formulaic
} derivation rather than the pointer-driven method may subject you to
} protests of “Cheater, cheater, pumpkin-eater!” from the test
} population.)

Google Groups: rec.arts.tv.soaps
DOOL: TAN: What do Nelson Broat and Milli Vanilli have in common?
Joanna L. Castillo
10/7/92
(...)
Ahhh...now all is clear.  What a cheater.  Cheater cheater pumpkin eater!

Google Books
Making a Difference:
Canadian Multicultural Literature
By Smaro Kamboureli
New York, NY: Oxford University Press
1996
Pg. 521:
‘You’re a cheater, cheater pumpkin-eater! I chose to bat first!’ I yelled.

Newspapers.com
18 May 1996, Stevens Point (WI) Journal, “Time for alert strip evolution” by Justin Isherwood, pg. 4, col. 2:
At 20 mph over the message becomes “posthumous, posthumous, posthumous” or “cheater, cheater, pumpkin eater.”

31 October 1996, Fort Worth (TX) Star-Telegram, “The Great Star-Telegram Pumpkin Carve-Off,” pg. E1, col. 3:
Patricia Rodriguez/Cheater, cheater, pumpkin eater

Urban Dictionary
cheater cheater pumpkin eater
it’s what little kids say when they suspect that one is cheating in a game.
kid: *takes TWO turns :O*
another kid: hey you can’t do that! you are a CHEATER CHEATER PUMPKIN EATER!
#cheeter#pumpkin#cheater pumpkin eater#eater#children
by ohmyfuckingod July 26, 2010