First I am not an attorney, so take this with a grain of salt. I believe that you are able to carry in a FL state park as of last year when the legilature passed a law allowing it. I am not sure what you mean by a Regional park, though.
I don't believe you can right now, but I think I've seen something as recent as this week, where there will be new laws in effect on July 1st. I think they've quite liberalized (the good kind) carry laws in state entities.