Green’s Dictionary of Slang

(Aus./N.Z.) a taxi.

1967		‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xl 4/5: slapsie: Taxi. From the rhyming slapsie maxie.
1983		R. Aven-Bray Ridgey-Didge Oz Jack Lang 10: He threw out his Warwick Farm to hail a slapsie.
1999		G. Seal Lingo 91: A slapsie maxie is a taxi.
2003		McGill Reed Dict. of N.Z. Sl.