Papua New Guinea had a sub-ICAO code of AY when it was administered by Australia. We used A followed by the FIR code such as S=Sydney, B=Brisbane. (eg Brisbane = ABBN, Sydney = ASSY)
PNG became independent on 16 Sep 1975 and retained the sub-FIR code AY (see Jackson Field, Port Moresby which is still AYPY)
I do not know when Australia decided it needed a separate code, the FS guys would have a better idea, being involved in message addressing. I would guess that it would have occurred when we updated our AFTN machinery.
I imagine that there were not many letters left so we chose Y.