This is a carol I always enjoyed singing, but we need to get a couple of grammatical points straight. Because look at that comma: there are no "merry gentlemen" here.
The historic meaning of the phrase "God rest you merry" is "may God grant you peace and happiness".
And if you see the title printed as "God rest ye..." then it's phoney archaism.
Glad we've sorted that. It's what Christmas is all about.
"Ye" would never have been correct, because "ye" is a subjective (nominative) pronoun only, never an objective (accusative) pronoun.