I don't know Modern Greek, but I do know that the pronunciation has changed. The rich vowel system of Ancient Greek has collapsed and simplified. οι is pronounced like English "boy" in Koine/Ancient Greek, but Modern Greek has collapsed all the old diphthongs into simple vowels. If you really think about it, why would the Greeks create a writing system with multiple ways of representing the same vowel sound? They didn't... no one does. As with English, the phonology of the language changed while the orthography and spelling remained the same. οι, ει, αι, ου, ευ, αυ represented vowel sounds distinct from both each other and the simple vowels α, ε, ι, ο, υ, η, ω. Even in Koine the vowels were starting to simplify, but this process has progressed significantly since Koine.
In Modern Greek ειρηνη is pronounced like ιρινι because of vowel simplification. In Ancient Greek this word has two vowel sounds (ει, η) which are distinct from ι. In Modern Greek ει, η, και ι represent one sound. ει was a diphthong pronounced like English "day". η was similar to ει but was a simple vowel and not a diphthong. It was pronounced like the long e of Latin or like the e in Spanish de which is not a diphthong (it's not pronounced like English "day"). English doesn't have an example of this sound as far as I know (English has a strong tendency toward diphthongs).
If you want to learn the more accurate pronunciation, don't use a tool designed for Modern Greek.