Green’s Dictionary of Slang

buckeen n.

[Anglo-Irish buckeen, a younger son of the impoverished Anglo-Irish aristocracy. The term apes the better-known squireen, a petty landowner]

a bully.

[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]M. Leeson Memoirs (1995) III 190: In consequence of [...] some buckeens there, that became troublesome, we resolved to shift the scene, and return to Pitt-street.
[UK]Lex. Balatronicum.
[Ire]T.C. Croker Fairy Legends and Traditions of the South of Ireland (1862) 327: Manus O’Rourke, a great buckeen, a cock-fighting, drinking blackguard that was long ago.