I don't know what the "best" way is, but one thing to do is to change the way we categorize that buyer. They may be qualified, but until they acknowledge the reality of the marketplace, they are not serious!
Almost always, these types of head-butting situations have to do with a difference in communication styles. So, perhaps you've been telling them, well, that doesn't make sense, the sellers aren't going to come down that much, et cetera. Maybe instead, just hand them listings of pending sales in their price range. "I just thought you'd like to know what's been selling recently!" Let them figure it out on their own!
Or, the other 'way round. Point being, sometimes we keep talking to them in the same way, waiting for different responses. If we change things around a little, maybe they'll respond differently!
All the best,