Green’s Dictionary of Slang

1. (Aus.) to throttle around the neck.

1871		Goulburn Herald (NSW) 20 Dec. 2/5: The villain in the latter instance put on what is termed in their slang, the ‘Maginnis’ pretty strong, as the throat is so much swollen as to almost prevent swallowing.
1901		Sydney Sportsman (Surry Hills, NSW) 21 Aug. 4/1: There is no guarantee that his new opponents, the garroters, will not put ‘Maginnis’ on him, half break his neck, and clean his pockets out.

2. (Aus.) to put in a position from which there is no escape, to pressurize; thus crooked maginnis, an unfair form of control, e.g. (moral) blackmail.

1900–10		Stephens & O’Brien Materials for a Dict. of Aus. Sl. [unpub. ms.] 103: MCGINNIS – PUTTING THE, ON: to put any opponent or combatant hors-de-combat. A grip or hold that cannot be unlocked or resisted.
1945		Baker Aus. Lang.