Green’s Dictionary of Slang

the stomach.

1824		Pierce Egan’s Life in London 26 Sept. 5/2: Matthew, rather irritated, gave a terrible plunge on his Lordship's digester, which made him a little pipy.
1904		Sydney Sportsman (Surry Hills, NSW) 15 June 5/2: the couple of left-handers that James sent into the digester of his adversary.