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You can. If you give to a baron/bishop/mayor the county title, his barony/city/bishopry will be the capital of the county.
 
True, But if you want to maintain control of the county that becomes a problem.
You can try it with your heir. For example give him city, give him county. City should become capital. It should be completed on the next succession. But that is just theory. I haven't tested it.

Edit: Or someone who will die soon and you will inherit.
 
What if you revoked the title from the baron who holds your desired capital and then gave the other baronies in the county to barons, so you only keep the capital-to-be as your direct holding? Wouldn't that switch the capital to whatever you are leftwith?