Are there any countries that recognize the Queen as their monarch but are not part of the Commonwealth of Nations?

While there are countries which are members of the Commonwealth without recognising Queen as their head of state, like India, which is a republic and Malaysia, which has its own monarchy, there are no countries which recognise the Queen as their monarch without being members of the Commonwealth.

There is no precedent for a former British colony retaining the monarch as its head of state while not joining the Commonwealth, as most countries which have gained independence from the United Kingdom have chosen to remain in the Commonwealth, even if they later decide to become republics.

Although the British Crown Dependencies and Overseas Territories are not part of the United Kingdom, nor are they separate members of the Commonwealth, except when participating in the Commonwealth Games, and are not separately represented at the Commonwealth Heads of Government Meetings.

I'm going to go for it . I'll say no . Such a country would be a Commonwealth realm so by definition be in the Commonwealth .

Some of the smaller British islands might have no representation in the Commonwealth by themselves ( except at the games ) and of course countries like Scotland , Wales , Northern Ireland and indeed England have no representation by themselves ( except at the games ) but their representation is carried by a bigger political unit , the UK . There maybe similar situations around the world to that but that's the best I can do .

The Isle of Man and the Channel Islands recognise the Queen as monarch, but are not part of the United Kingdom and are not listed as members of the Commonwealth in their own right.