Harold Courlander's 1963 book Negro Folk Music, USA (New York, Columbia University Press; pp. 149-150) contains three counting out children's games which are very similar to "Who Stole The Cookie". These games are included in the chapter "Ring Games And PlayParty Songs". For the record (no pun intended, here are the words and comments to those games:

record (no pun intended, here are the words and comments to those games:
"In one American ring game, each player has a number; when his number is called by the leader he must respond with an appropriate answer without becoming rattled, and then pass the play on to another individual. If a player gives the wrong response, he is counted out of the game. Thereafter, his number cannot be called, as he is no longer a participant; should someone call his number in the heat of play, he too goes out. The repartee is half-sung-more properly, called, with stylized inflections-to the accompaniment of rhythmic clapping.
[My note: The first example is given without any title]
All Together: One two three and a zing sing sing.
Leader: Number one.
Number One: Who, me?
Leader: Yes, you.
Number One: Couldn't be.
Leader: Then who?
Number One: Number five:
Number Five: Who, me?
Leader: Yes, you.
Number Five: Couldn't be.
Leader: Then who?
Number Five: Number nine:
Number Nine: Who, me?
Leader: Yes, you.
Number Nine: Couldn't be.
Leader: Then who?
Number Nine : Number Two:
Etc.

**

Another American variant is:

"Who Took The Cookie From The Cookie Jar"

All Together: Who took the cookie from the cookie jar?
Leader: Number One took the cookie from the cookie jar.
Number One: Not me took the cookie from the cookie jar.
Leader: Then who took the cookie from the cookie jar?
Number One: Number Seven took the cookie from the cookie jar.
Number Seven: Not me took the cookie from the cookie jar.
Leader: Then who took the cookie from the cookie jar?
Number Seven: Number Ten took the cookie from the cookie jar.
Etc.

-snip-

Courlander adds this comment and example:

"A Haitian version of the game, with similar counting out rules, is known as "Uncle Pierre". Each player is given a name specifying a certain number of sheep-Four Sheep, Ten Sheep, Six Sheep. etc. As translated from the Creole, the repartee goes:

Leader: Uncle Pierre went to my farm and took seven sheep
Seven Sheep: Tomanitor
Leader: How many sheep did he take?
Seven Sheep: Nineteen Sheep
Nineteen Sheep: Tomanitor
Leader: How many sheep did he take?
Nineteen Sheep: One sheep
One Sheep: Tomanitor
Etc.

[Ibid]

-snip-

I don't know what "Tomanitor" means and I didn't reproduce the pages that included Courlander's footnotes for these examples. Presumably, a definition for "Tomanitor" is included in those footnotes.