Well, that certainly fits the OP. So, let's suggest a continued persecution of Christians within the Western Empire at least. Roman Paganism prevails, and Christianity spreads throughout the Middle East and perhaps into East Africa.
Now, how would this change the face of the Migration Period, if at all? With Christianity ebbing away at Persia and into Central Asia, would it have a profound affect on the Pagans who swept into Europe? Would we still see Germanic or Norse Paganism in Central and Northern Europe, or is it likely that these groups would see some Christianisation before the migrations started?