Green’s Dictionary of Slang

conky adj.

also conkey
[conk v.2 (1), i.e. ‘knock about’, strengthened by conk (out) v. (1)]

sub-standard, second-rate.

[UK] ‘’Arry on Arrius’ in Punch 26 Dec. 303/2: Your Cockney eternal? No doubt! [...] / It’s much more than your conkey old Classicks, for they ’ave about ’ad their day.
[Aus]Truth (Sydney) 19 Feb. 3/7: Well, he were a conkey feller / In his own small tlnpot way.
[Aus]N. Pulliam I Travelled a Lonely Land (1957) 232/1: conky – no good.