Green’s Dictionary of Slang

(Aus.) the small piece of wood used for tossing the coins in the game of two-up.

1945		Baker Aus. Lang.
1949		I.L. Idriess One Wet Season 146: The only music to Womba was the clapping of the kylies. [Ibid.] 205: The didgeree-doos boomed, wommeras and kylies clicked rhythmically.
1999		G. Seal Lingo 150: [in two-up] a kip (or stick, bat, or kylie) is the wooden bat or spatula-like device used to throw the pennies into the air.