When do the earliest rhymes appear in Koine or Medieval Greek?

1. Did the Greeks rhyme?
2. Did Latin poetry rhyme?

Did the Greeks rhyme?

History of Rhyme

Ancient Greek and Roman poetry did not rhyme, and early European poetry did not rhyme either. In the West, rhyme began to emerge during the medieval period.

Did Latin poetry rhyme?

it's true that, because Latin is an inflected language and has a lot of freedom with word order, Latin poets tend to avoid rhyming.