The adjective sly is used to mean secret, covert, clandestine.

And the phrase on, or upon, the sly means secretly, covertly, clandestinely. For example, the following definition is from A Vocabulary of the Flash Language, a glossary appended to Memoirs of James Hardy Vaux (London: Printed by W. Clowes, 1819), by James Hardy Vaux (1782-1841?), an Englishman who was convicted and transported to Australia on three separate occasions:

SLY. Any business transacted, or intimation given, privately, or under the rose ¹, is said to be done upon the sly.

¹ The phrase under the rose means privately, in secret.

The term sly trade occurs in Of the Character of Books of the Street-sale, in London Labour and the London Poor; A Cyclopædia of the Condition and Earnings of Those that Will Work, Those that Cannot Work, and Those that Will Not Work (London, 1851), by the English journalist, author and social reformer Henry Mayhew (1812-1887):

The same informant told me that he had lived near an old man who died twenty-five years ago, or it might be more, with whom he was somewhat intimate. This old man had been all his life familiar with the street trade in books, which he had often hawked—a trade now almost unknown […]. “And I’ve heard the old man say, sir,” I was further told, “how he had to tread his shoes straight about what books he showed publicly. He sold ‘Tom Paine’ on the sly. If anybody bought a book and would pay a good price for it, three times as much as was marked, he’d give the ‘Age of Reason’ in. I never see it now, but I don’t suppose anybody would interfere if it was offered. A sly trade’s always the best for paying, and for selling too.”

In Australian English, the adjective sly has especially been used in:
– sly grog, denoting liquor sold without a licence;
– sly grog-shop, denoting a place where liquor is sold without a licence;
– sly grog-man, denoting a man selling liquor without a licence.
—Cf. meaning and origin of the word ‘grog’.

For example, the following is from the Torres News (Thursday Island, Queensland) of Monday 24^th February 2014:

This month a man from PNG on Saibai has been charged with selling ‘sly grog’. He was arrested with 80 litres of cask wine and charged with selling liquor without a permit.
He will appear in the Saibai Magistrates Court later this week.

These are, in chronological order, the earliest occurrences of the terms sly grog, sly grog-shop and sly grog-man that I have found:

1, 2 & 3-: From the Hobart Town Gazette, and Van Diemen’s Land ² Advertiser (Hobart, Tasmania):

1-: Of Friday 14^th January 1825:

In reference […] to the present system of licensing of refusing to license persons to retail wine, ale, and beer, it is our wish to offer some observations. That by restricting the licenses within a given number, any benefit to either the community at large or the Publicans in particular, is afforded, we are on due consideration bound to doubt; while that by it the interests of Government suffer, we hold as a fact completely indisputable. It is well known that more liquor and beer are vended in what are elegantly called “Sly Grog-shops,” than in all the Licensed Houses. It is equally well known that for one of these sly grog-shops, which becomes obnoxious to the Police and finably tangible, nine escape year after year, to the fortune-making pleasure of their lawless owners. Consequently, who need feel surprised that though the public-houses are deserted, a drunken populace reel to and fro? Every publican’s premises are open to the Police; his customers are exposed to observation; if they are prisoners, he must either turn them out when the bell rings, or be heavily fined; he must not allow gambling in any of his rooms; and even a rubber at skittles is punished with a penalty of £40 sterling!—Who therefore need be amazed that the lower orders consume their time and expend their money where, unrestrained by constables or a conscientious inn-keeper, they may swear and play at cards as much as they please, and as long as they chuse, because the sly grog-man is in their power! Now we state, without fear of refutation, that the present fine for keeping an unlicensed house is not at all adequate to the offence, when the immoral train of evils connected with it are considered;—that its inadequacy is proved by the alarming increase of offenders;—and that nothing short of imprisonment as well as an augmented fine, will tend to diminish the list of those, whose “sly grog-shops,” if not repositories for stolen goods, are at best but nurseries for blasphemy and lewdness! In brief, would it not be better to let even indifferent characters have licenses, which would certainly restrain them in some degree, and by which a considerable share of the Colonial Revenue would annually be furnished, than by persevering in the present restrictive system to prevent their paying that sum to Government; which, when they are discovered to sell without a lisense, they must pay as a forfeit into the hands of some grovelling informer?

² Van Diemen’s Land was the name of the island of Tasmania until 1855. Anthony van Diemen (1593-1645), Governor-General of the Dutch East Indies, sent the Dutch explorer Abel Tasman (1603-1659) on his voyage of discovery in 1642.

2-: Of Friday 18^th March 1825:

Our Readers will gladly perceive, by an Act of Council which will be published in our next, that the Colonial Legislature have most properly suspended so much of a previous Law or Ordinance, as rendered the signature of a parochial Minister in New South Wales and Van Diemen’s Land respectively, a requisite to every victualler’s certificate, for grounding his claim to a beer or spirit license. When we first read that Ordinance it very forcibly struck us as altogether non-calculated to effect any benefit; but, as admirably tending by palpable and inevitable instrumentality to produce three, if not more, positive disadvantages. We knew that if one class of colonial tradesmen had peculiar reasons for feeling dissatisfied at the harsh restrictions imposed on their efforts—that class consisted of the publicans; who, viewed on the aggregate were respectable, by whom the local Revenue was in no trifling degree augmented, but against whose fair and highly-paid-for chances of success in business, the most litigious surplusage of restraint was customary. We were sure that as a direct consequence of such restraint their hopes of honourable recompence [sic] for incessant toil and utter deprivation of domestic comfort, had become almost extinguished. And we therefore felt convinced that in the sequel they would altogether decline applying for licenses, whilst many of them would become sly grog-men to the manifest injury of Government.

3-: Of Friday 10^th June 1825:

Port Dalrymple News.

Extracts from the Letter of our Launceston Correspondent, dated the 6^th instant:—
“The use of a free Press is conspicuous in more instances than can be mentioned, and even here your Paper is of service, for a Distraint has issued for the sly-grog fines, in consequence of your exposition, against the great man at Tallisker; but he swears he will appeal to Head Quarters, and that the liquor was unlawfully sold without his knowledge, and contrary to his consent.—This, however, I know to be false!”