There were 13 colonies plus Vermont, they all issued paper currency, so did the Continental Congress and they probably all issued $2 notes, possibly in several series. So if you are asking about paper money then the answer is yes they exist. If yo are asking about a $2 coin no they don't. And if you are asking if there was ever legislation (a bill) relating to a $2 coin then I have no idea. Can you be more specific?