Doesn't it seem likely that Shakespeare was making a joke? Instead of saying simply "Great Ones" (which I think was a set phrase then, as it still is today, for the privileged in society), he was poking fun at such folks by appending the suffix -yer, as if being a Great One was not about character or moral stature, it was simply a profession, like that of lawyers and sawyers. In other words, might not oneyer be a Shakespearean madeupical?
The O.E.D. says the origin is uncertain, the meaning is perhaps 'a sheriff', and it's now used only in allusion to Shakespeare's 'great Oneyres'. However, it does seem to be sure that the -yer is the same as in lawyer; great oneyer is given as an example under the entry for the suffix.