Green’s Dictionary of Slang

(Aus.) a prison, a police lock-up.

1896		Truth (Sydney) 21 June 5/1: [I]nside ten minutes from the time he ‘flew the flimsy’ the fellow was in the ‘bulliang’ on a charge of obtaining live pounds by a false pretence.
1898		Truth (Sydney) 4 Sept. 7/2: [headline] LARKS IN LIMBO! / BATTLES IN THE BULLIANG / A full and Authentic account of the Riots in Maitland Gaol.
1900		Truth (Sydney) 14 Jan. 7/5: The boy’s experiences in this precious prison are worthy of a Chinese limbo, and would shame and disgrace a South Sea bulliang.
1904		Sydney Sportsman (Surry Hills, NSW) 17 Aug. 3/4: There's a she-lunatic [...] knocking around Sydney Just now, and first she knows she’ll be in the bulliang.
1921		Sydney Sportsman (Surry Hills, NSW) 6 Apr. 7/7: Some bleater queered their pitch, and the bloke slipped back on his tracks, caught one imp in the act, and actually rushed him off to the bullyang.