Green’s Dictionary of Slang

nicely adv.

[response to the question, ‘how are you feeling/doing?’]

(Irish) a euph. for drunk(enly).

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[Ire](con. 1940s) J. Healy Death of an Irish Town 18: Himself, with the reins in hand and ‘nicely’, called out: ‘Come on, woman’.
[Ire]Sun. Trib. (Dublin) 27 Oct. n.p.: Norma was ‘nicely’ was how her friend described Norma’s condition after what seemed like respectable, quiet party [BS].