I've spoken elsewhere of the importance of the institution of the Crown as opposed to the minor relevance of the person of the monarch.
An elected monarchy would be the simplest way to go. But we would have to exercise care in deciding who could stand - remember the 'Boaty McBoatface' business? Sometimes we Brits will do something silly for the sake of it and King David Beckham, or His Majesty Graham Norton would be a bit beyond. Popular for the right reasons, like David Attenborough or Trevor McDonald, for instance. Anyone with sufficient dignity or gravitas.
The added advantage would be that the King or Queen of England, if elected, and whatever colour they were, would at least be English! Dont know about you, but I'm getting fed up of being 'ruled' by foreigners!