Unlike the Old Testament, which was written over several hundred years, the New Testament was written in a relatively narrow span of time, probably less than a century, from around 65 to 150 CE.
"Koine Greek is not only important to the history of the Greeks for being their first common dialect . . ., but it's also important . . . for being the first 'international' form of speech, and eventually the chosen medium for the teaching and spreading of Christianity. Koine Greek was unofficially a first or second language in the Roman Empire."