So for the last six weeks I’ve been studying Koine Greek, with a goal of being able to read the Stoic texts for myself without the help of a translator.
There are two main pronunciation schemes for Koine, the Erasmian (an academic teaching pronunciation) and the pronunciation scheme of modern Greek. My instructor uses the latter.
Until Gregory Wasson, most of the resources Koine learners have available is within the context of the Christian New Testament. However, you’ll find many of the words of the Stoic lexicon there.
If you’re interested in what Koine sounds like with a modern Greek pronunciation from a native speaker of Greek, this YouTube channel is a treasure trove.
I’ve been using it to aid in my own pronunciation and listening exercises.
You’ll hear words like ‘pneuma’ /ˈpnɛv.ma/), and other terms like it.
I’m not sure if this fellow has gotten to Romans, as Pauline Ethics are full of Stoic terms, that would be very close to our interests. (EDIT: he has)
Anyhoo… enjoy!
Mountain Stoic 
Excellent study, but why so much emphasis on pronunciation when you only want to read or follow a translation.
I’m using two methods, one is conversational with very little focus on grammar. The other is more rigorously based on syntax and grammar. So for the one class, it’s almost entirely aural slash oral.