I'm sorry to hear that you weren't able to get in at Cinderella's Royal Table, Laura. Rest assured, though, that there are plenty of other great choices!
Chef Mickey's is a very popular choice. It is a buffet restaurant located in Disney's Contemporary Resort. If the little girl in question has her heart set on meeting princesses, perhaps a meal at
Akershus Royal Banquet Hall is in order. In all honesty, I prefer that breakfast over the one in Cinderella Castle; it seems to have more of a laid back atmosphere, in my opinion. My last suggestion is also an Epcot restaurant.
Garden Grill is a family favorite for us. We love the unique spin (pun intended) of dining in a restaurant that actually rotates throughout the course of the meal. So, too, are we partial to the family-style menu served there; did you know that some of the menu items are grown right there in The Land pavilion? That's cool, right? I bet your nine-year-old would think so, too. Good luck with your decision!