One Roman writer, Thallus, apparently acknowledged the darkness. He explained it as an eclipse of the sun, presumably to discredit the Christian claims of a miraculous event. Thallus' work is believed to have been written about 52 AD, so it is an important witness to early knowledge of the darkness to the extent we can validate the claim that Thallus wrote about it.
Unfortunately we have none of Thallus' actual words, and only a brief quote from Africanus (about 220 AD) who pointed out that the solar eclipse claim was wrong.
Here is how one site describes Thallus' testimony:
Thallus, a historian writing in AD. 52, wrote to deny any supernatural
elements accompanying the Crucifixion . Though his writings are lost
to us, we have the quotations of other later writers. The writing of
Thallus shows that the facts of Jesus’ death were known and discussed
in Rome as early as the middle of the first century, to the extent
that unbelievers like Thallus thought it necessary to explain the
matter of the darkness as something natural. He took the existence of
Christ for granted. Neither Jesus, nor the darkness at his death, were
ever denied. At the time of his writing, unbelievers had already been
explaining the darkness at the time of the Crucifixion as a purely
That page also mentions Africanus who commented on Thallus and also quoted Phlegon of Tralles who recorded the date of an event of darkness.
For a much better "chain of evidence" demonstrating the probability of Thallus' comments, see William Lane Craig on the subject.
According to Dr. Craig, Georgius Syncellus' Chronicle from about the year 800 quotes church father Julius Africanus as writing:
On the whole world there pressed a most fearful darkness; and the
rocks were rent by an earthquake, and many places in Judea and other
districts were thrown down. This darkness Thallus in the third book of
his History, calls, as appears to me without reason, an eclipse of the
sun. For the Hebrews celebrate the Passover on the 14th day according
to the moon, and the passion of our Saviour falls on the day before
the Passover; but an eclipse of the sun takes place only when the moon
comes under the sun. And it cannot happen at any other time but in the
interval between the first day of the new moon and the last of the
old, that is, at their junction: how then should an eclipse be
supposed to happen when the moon is almost diametrically opposite the
sun? Let that opinion pass however; let it carry the majority with it;
and let this portent of the world be deemed an eclipse of the sun,
like others a portent only to the eye. Phlegon records that, in the
time of Tiberius Caesar, at full moon, there was a full eclipse of the
sun from the sixth hour to the ninth—manifestly that one of which we
speak. But what has an eclipse in common with an earthquake, the
rending of rocks, and the resurrection of the dead, and so great a
perturbation throughout the universe? Surely no such event as this is
recorded for a long period. But it was a darkness induced by God,
because the Lord happened then to suffer.
I have not determined to what extent Phlegon's work might be an independent verification that unusual darkness occurred, and when. He does give a year which should be convertible, but first we would need to evaluate the evidence that he was accurately quoted by Africanus and others.