When Does "Coriolanus" (1608) Take Place?
"The Tragedy of Coriolanus" (often released simply as "Coriolanus") is a historical fiction stageplay written by William Shakespeare and performed as early as 1608 (according to most scholars). So when is "Coriolanus" set?
It takes place in the years:
We know this because Rome is presented as a small city-state republic (no longer a kingdom; but not yet the huge empire it will become) and is sometimes at war with other city-states in what will become Italy eventually in 1861 AD. Therefore it must be between 509 BC and 27 BC.

494 BC - 488 BC
We know this because Rome is presented as a small city-state republic (no longer a kingdom; but not yet the huge empire it will become) and is sometimes at war with other city-states in what will become Italy eventually in 1861 AD. Therefore it must be between 509 BC and 27 BC.
More specifically, in act 1 scene 1, when the real-world Roman politician Menenius Agrippa asks, "What is granted them?", Caius Marcius (based on the real-world General Gaius Marcius Coriolanus) replies, "Five tribunes to defend their vulgar wisdoms, / Of their own choice." Marcius is referring to the creation (or "grant"ing) of a new political office open only to common (or "vulgar") folk called the tribune of the plebs. This happened in the real world in 494 BC.
Then, between act 1 scene 7 and act 1 scene 8 of the play, the Roman army attacks a town named Corioles (or Corioli) of the real-world Volsci tribe and Marcius leads the small regiment which makes the decisive winning move, breaking through the town gates. In his words, "Alone I fought in your Corioles' walls". In act 1 scene 9, the real-world Consul Postumus Cominius Auruncus agrees, "Therefore be it known, / As to us to all the world, that Caius Marcius / Wears this war's garland" (i.e. holds this war's position most worthy of military decoration) and re-christens Caius Marcius as Caius Marcius Coriolanus in appreciation. This occurred in the real world in 493 BC.
Partway through the show, in act 3 scene 1, food riots break out in Rome during which Marcius publicly rails against the tribune office, "Behold, these are the tribunes of the people, / The tongues o’ th’ common mouth. I do despise them". Soon after, in act 3 scene 3, Marcius is exiled for his anti-republic/anti-democratic views. This is contested history but it's believed the real-world Marcius a.k.a. Coriolanus did argue in favor of abolishing the recently created tribune of the plebs office during grain riots and was then exiled from Rome for it in 491 BC.
Near the end of the narrative, in act 5 scene 3, the audience is shown a narrowly-won peace between the Volsci and the Romans brokered by the traitorous exiled Marcius at the urging of his mother and his wife. This is believed to have happened in the real world in 488 BC.
The final scene, act 5 scene 5, is unplaceable as it depicts only one version of later events in Marcius' life, which are unknown to history.
It was remade in 1962.
It was adapted to TV in 1963, as an opera in 1974, to TV again in 1983, and, finally, to film in 2011.