I have mixed feelings about this and even considered drawing up plans in the past to see if any venture capitalists were interested in a small theme park.
Our weather is better than Dollywood's and they are open 10 months out of the year. There is no reason that a park in the Charlotte market couldn't be open 10 months a year. In order to do that, though, it needs a great mix of family-friendly attractions to draw on a larger demographic of the market place to draw people to it when temperatures started dropping.
With that being said, due to the size and history of Carowinds, I would be have a hard time believing that the market would allow another park the size of Carowinds to be successful. I could see a 'Fun Spot America' type park with a couple of coasters and a nice mix of flat rides succeed. Especially if it was open a majority of the year.
EDIT: I agree with Jonathan that Raleigh could support an amusement park.