Green’s Dictionary of Slang

earl of Cork n.2

also duke of Cork
[rhy. sl.]

1. a talk.

[US]St. Vincent Troubridge ‘Some Notes on Rhyming Argot’ in AS XXI:1 Feb. 46: duke of cork. A talk; a walk. (English.) Agreed as English, but always Earl of Cork. This corresponds to an actual title in the British peerage, held by a well-known and definitely eccentric noble man during the period (1870–1890) of the maximum growth of rhyming slang.
[US]Wentworth & Flexner DAS.

2. a walk.

see sense 1.