With a POD after the start of the Reformation (for the sake of convenience, say, after Martin Luther's death in 1546), what trends or developments might lead to a more significant presence of non-trinitarian Christian doctrines? They needn't be a majority or plurality in any one country, though that would certainly be a plus.
Well, Unitarian theology was pretty common in the US around the time of independence. There were serious movers in the very early Episcopal church there, wanting to drop the Trinity. (Speaking as an Episcopal: GAAAAA!!!!)
A lot of the Founding Fathers were Deists or pretty Unitarian leaning Christians. (Every time I hear the Tea Party Republicans going on about 'returning to the faith of the Founding Fathers', I am amused that they are advocating the Unitarian church without knowing it....)
Poland had a pretty strong Socinian movement for a while, which I have heard claimed was like Unitarianism.
Then, of course, much later you have people like the Jehovah's Witnesses who are essentially Arian, denying the divinity of Christ. Not that they could be big enough to be an answer to your challenge.