Green’s Dictionary of Slang

carney n.¹

soft, hypocritical talk.

1818		W. Perry London Guide 205: The thoroughbred sycophant may be known by his carney, or small talk, or by his whining.
1823		‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 21: Carney — Love tales; also supplicatory intercessions, whereby the auditor is made to believe he has several virtuous attributes that he never before dreamt of possessing [...] ’Tis a word of Irish extraction, and first cousin to blarney.
1841		‘The Musical Coalheaver’ Dublin Comic Songster 98: And I’ve been told by an old pal, / And I don’t think it’s carney, / That she can sing the ‘Oyster Gal,’ / As well as Caterlarney.
1846		Bell’s Life in Sydney 14 Mar. 1/6: There was one who would not stand his ‘Carney,’ Nor his ‘flummery,’ used at Killarney.
1859, 1860		Hotten Dict. of Modern Sl. etc.
1864, 1867, 1870		Hotten Sl. Dict.
1877		‘Mister Barney’ in Laughing Songster 127: Och! Mister Barney, / None of your carney.
1881		Newcastle Courant 2 Sept. 6/5: He has an oily jibb and is as good at carney as a cackle tub chicken.

In phrases

come the (old) carney (v.)

to flatter.

1923

J. Manchon Le Slang 79: To come the carney, flatter, flagorner.