After the question of Dougsmit in another thread, I searched in my barbarian imitations (the Roman ones), and found about eight left facing coins. Here's four of them. All well-known 4th century types.
Yes, these are all nice barb coins of the Constantinian period but none are Barbarous Radiates. Later official coins are more often found left facing also.
Ah, I had missed the 'radiate' in your post. Of my (about) 50 barbarian Romans (barbaric? barbarous? what's the right term?), some 20 are radiates, all of them with Eyes Right. I have one Augustus looking left, the ten other Lefts have more or less been copied after 4th century coins. My avatar coin is one of these, I turned it right because I wanted it to look benignly at the text I write.