I found this interesting reference in an article in the American Chronicle. There was no source quoted but it sounds like a typical Roman legend:
The name [of amethyst] is Greek for "sober." Now, this makes sense once you hear the story of Bacchus. He was the Roman god of wine and revelry. One day, he was in a foul mood and set his tigers on the next person to cross his path. This unlucky person happened to be a maiden named Amethyst who was on her way to the Goddess Diana's temple. Diana turned her into a pillar of quartz to stop the tiger attack. Bacchus was so remorseful; he poured wine over the pillar as an apology and stained the pillar purple.
As a result, the stone was believed to have the power to stave off drunkenness. In fact, the ancient Greeks and Romans would carve drinking goblets from the violet quartz rather than wear them as amethyst and diamond rings, in an attempt to remain sober as they drank their wine.
I found a reference to amethyst cups, though, in the book "Roman Life In The Days of Cicero" by Alfred John Church. Apparently, the corrupt governor of Sicily, Verres, ripped off the amethyst cups of good king Antiochus:
The dining-room and table were richly furnished, the silver plate being particularly
splendid. Antiochus was highly delighted with the entertainment, and lost no time in returning
the compliment. The dinner to which he invited the governor was set out with a splendour
to which Verres had nothing to compare. There was silver plate in abundance, and there
were also cups of gold, these last adorned with magnificent gems.
Conspicuous among the ornaments of the table was a drinking vessel, all in one piece,
probably of amethyst, and with a handle of gold. Verres expressed himself delighted with
what he saw. He handled every vessel and was loud in its praises. The simple-minded
King, on the other hand, heard the compliment with pride. Next day came a message. Would
the King lend some of the more beautiful cups to his excellency ? He wished to show them
to his own artists. A special request was made for the amethyst cup. All was sent without a
suspicion of danger.
But the King had still in his possession something that especially excited the Roman's cupidity. This was a candelabrum of gold richly adorned with jewels. It had been intended for
an offering to the tutelary deity of Rome, Jupiter of the Capitol. But the temple, which had
been burnt to the ground in the civil wars, had not yet been rebuilt, and the princes, anxious
that their gift should not be seen before it was publicly presented, resolved to carry it back with
them to Syria. Verres, however, had got, no one knew how, some inkling of the matter, and
he begged Antiochus to let him have a sight of it. The young prince, who, so far from being
suspicious, was hardly sufficiently cautious, had it carefully wrapped up, and sent it to the
governor's palace. When he had minutely inspected it, the messengers prepared to carry
it back. Verres, however, had not seen enough of it. It clearly deserved more than one
examination. Would they leave it with him for a time ? They left it, suspecting nothing.
Antiochus, on his part, had no apprehensions. When some days had passed and the candelabrum
was not returned, he sent to ask for it. The governor begged the messenger to come
again the next day. It seemed a strange request; still the man came again and was
The King himself then waited on the governor and begged him to return it. Verres hinted, or rather said plainly, that he should very much like it as a present.
"This is impossible," replied the prince, " the honour due to Jupiter and public opinion forbid it. All the world knows that the offering is to be made, and I cannot go back from my word."
Verres perceived that soft words would be useless, and took at once another line. The King,
he said, must leave Sicily before nightfall. The public safety demanded it. He had heard of a
piratical expedition which was on its way from Syria to the province, and that his departure
was necessary. Antiochus had no choice but to obey ; but before he went he publicly protested
in the market-place of Syracuse against the wrong that had been done. His other
valuables, the gold and the jewels, he did not so much regret ; but it was monstrous that he
should be robbed of the gift that he destined for the altar of the tutelary god of Rome. -Roman Life in the Days of Cicero: Sketches Drawn from His Letters & Speeches,By Alfred John Church,Published by Macmillan, 1895.