I've come across something interesting. Following the clue that the original is of Scottish origin and plugging the nonsense words into the Dictionary of the Scots Language, I found that "kie" means "key" and that there was (maybe still is) a tradition where Scottish children would hold up a hand to indicate that the "key" was in the "lock" to request a recess during a game. IF that is the origin, then the "won't you kie me, o" would mean "I need a break!"

Kie - 2. In pl.: a state of, or call for, truce in a children's game (Fif.17, w. and sm.Sc. 1959). Cf. Barley. Also in dim. forms keysie, keysies (keysie ne.Sc. 1990s; keysies Edb. 1960s).
Gsw. 1900–38 per Fif.17:
A call for a truce in a game added to the gesture of holding up the hand with the fingers crossed or with the thumb sticking out between the first and second fingers. Also called Key's locked!
https://dsl.ac.uk/entry/snd/key