Green’s Dictionary of Slang

quoit n.

[it is ‘round with a hole in it’]

1. (Aus./N.Z., also coight, coit) the anus, the buttocks; thus go for one’s quoit(s), to hurry.

Yellow Rag in P. Adam-Smith Folklore of the Aus. Railwaymen 236: STEWARD’s CHORUS / We expect our Upright Grand Instrument out by this afternoon’s delivery. Also, Quoits, Balls, and Games / FUN FOR EVERYONE / that can make fun.
[Aus]Baker Popular Dict. Aus. Sl. 58: Quoit, the buttocks.
[Aus](con. 1941) E. Lambert Twenty Thousand Thieves 95: See those jokers sitting on their quoits over there?
[Aus] ‘Whisper All Aussie Dict.’ in Kings Cross Whisper (Sydney) xxxviii 10/3: quoit: Backside.
[Aus]R.G. Barrett You Wouldn’t Be Dead for Quids (1989) 128: You’ve been tight as a tom-cat’s quoit since the day you were born.
[Aus]S. Maloney Something Fishy (2006) 18: You know much i enjoy sitting on the backbench with my thumb up my quoit.
[Aus]S. Maloney Sucked In 52: We’d better be ready. not sitting around with cobwebs up our quoit.
[Aus]N. Cummins Adventures of the Honey Badger [ebook] The poor girl was walking on the old boy’s back while hanging onto the tops of the partition and misjudged her step while working on the coight region.
[Aus]N. Cummins Adventures of the Honey Badger [ebook] You couldn’t drive a pin up his arse with a sledgehammer. Mate, he is as tight as a fish’s coit.

2. (Aus.) a fool.

[Aus]Baker Aus. Lang. 130: Fools of one kind and another have carved a considerable niche for themselves in Australian speech and little explanation is needed for any of the following: lardhead, loop, nit, plat (a clipping from platypus), quoit [etc.].

In phrases

go for one’s quoits (v.) (also go for a lick of one’s coit) [? fig. use of quoit n.]

(Aus.) to run fast, to work hard, to make one’s best effort.

[Aus]Baker Popular Dict. Aus. Sl.
[Aus]J. Cleary Sundowners 42: Going for the lick of his coit up the street.
[Aus]S. Gore Holy Smoke 80: Away they go for their quoits – flat out like a lizard drinking.