Your challenge is to have the USA, after the revolution decide to have a King. Then have them choose one of the royal families who lost their thrones in Europe. They could just be a figure head or have all the powers of a tsar. Please don't fill up the thread with reasons why it couldn't happen. I know it couldn't reasonably have happened, that's why its a challenge.
If you agree that this isn't reasonable, then why isn't this in ASB?
Moving on... let's see...
The trick is to have said royal family in the USA at the time of the revolution, even if it's just at the constitutional conventions.
It'd be awkward to be like "hey we just won our independence from european monarchy. What to do? Oh, I know! Let's import a european monarch!"
It's much better if we start from: "Well we have independence, but I'm not so sure about this republic idea. What we need is a monarch. And what do you know, Mr. Smith here is of noble heritage and suitable for a throne! How about you give up your claim on whateveria and become sovereign of America?"
There are only two ways I see a foreign host finding themselves on the American throne.
1. A war ousts them from power, perhaps an heir or a pretender stages a coup or presses a claim, and the sitting power is forced to flee. But why go to another hemisphere when you can camp in a friendly or neighboring realm to gather a host of allies to take back what it rightfully yours? Fleeing the continent is a bit extreme when there are usually other alternatives...
2. A revolution completely topples the monarchy and nobility of country and sends their entire elite class fleeing for their lives. Like in the French Revolution, only it has to happen before the American revolution. This sounds like the most promising scenario. The likely-hood of the crown being offered to this noble increases with these two conditions: A: That the noble in question be of culture that is either Anglophone or otherwise closely related to a large portion of the colonists' heritage. B: That a great many of the noble class follow the would-be king.
Hope this helps