Green’s Dictionary of Slang

press button n.

also pressie
[joc. mispron.; usu. Catholic use]

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

[UK] in C. MacInnes June in Her Spring in DSUE (1984).
[NZ](con. 1935) A. Campbell Island To Island (1984) 87: We’d gang up on the kids who chucked off at us — like the boys from the Catholic home. They’d call us ‘Pressbuttons’; we’d call them ‘doolans’.
[NZ]McGill Dict. of Kiwi Sl. 88/1: Pressbutton Presbyterian.
[NZ]McGill Reed Dict. of N.Z. Sl. 163: Pressbutton/Pressie A Presbyterian. ANZ C20.