You'd have to first define what you mean by "black market".

We have good documentation of smugglers in ancient Assyria. The British Museum, for example has a collection of cuneiform tablets which document the efforts of one family to evade taxes, smuggling goods like tin from from Anatolia. We've got record of correspondence of the patriarch Pushu-ken his sons some 4000 years ago, with discussions of when and how to take "the narrow track" -- that is the unposted route between Kanesh and Ashur through the mountains, free of checkpoints and tariffs.

The good sold themselves wouldn't be contraband -- tin could be legally sold-- but the proper tax wouldn't have been paid, presumably the penalty for such a transaction would have been substantial.

But if you're asking "what works were banned?" Things that were effectively banned may leave no trace, but we've got plenty of evidence of books being banned for the same reasons they might be now: politics, religion, sexuality. So, for example, Caesar Augustus' morality laws ban all sorts of lascivious material, and Ovid's work the Ars amatoria was banned. Amusingly, a translation of it was seized as obscene as late as 1930 by US Customs.

We've also got plenty of records of ancient piracy -- Julius Caesar himself has the celebrated story of having been capture by pirates. All their commercial dealings, by definition, would be illegal. One of the most common black market activities would have been the seizure of human beings and their ransom or sale as slaves-- in some instance that might have been legal, but in other instances wasn't

See:

Hartnett, Alexandra, and Shannon Lee Dawdy. “The Archaeology of Illegal and Illicit Economies.” Annual Review of Anthropology, vol. 42, 2013, pp. 37–51.

De Souza, Philip. “Rome's Contribution to the Development of Piracy.” Memoirs of the American Academy in Rome. Supplementary Volumes, vol. 6, 2008, pp. 71–96.