Green’s Dictionary of Slang

one who delivers supplies of contraband liquor.

1911		Truth (Wellington) 28 Oct. 4: It is possible to get as much liquor as one wants in Masterton, and while much of it [...] is of good quality, much more (surreptitiously dispensed at sly-groggeries and by what are locally termed ‘droppers’ at enhanced prices) is atrocious and harmful liquor [DNZE].
1949		F. Sargeson I Saw in My Dream 255: When the police raided her [...] they reckoned they’d got her this time, because they’d found out a dropper had been through the town just a few nights before on his lorry. So they reckoned she’d be well stocked up.
1976		J. McClenaghan Travelling Man 20: They could bring in their own liquor [...] and there was no reason why they should when they could rely on the droppers [DNZE].
1985		R.T. Hermans Capital Coppers 12: [The introduction of Nolicence to the Waiararapa] brought a new problem in the form of the sly grog seller (or ‘dropper’) [...] One well known ‘dropper’... used to plant his bottles under street culverts for his clients [DNZE].