The only resorts I can think of that use to allow pets (not sure about the current rules) were the Siverleaf resorts in Branson (Holiday Hills is one and I think Ozark Mountain is another). These exchange with RCI. With I.I. Stormy Point Village use to allow pets. However, this resort is split and has two management companies/developers (not certain if that's still true or not). One portion was developed by Festiva and the newest section is being developed by Summer Winds. I don't know if each management company has different rules of not.
At any rate, I'd call first. I'm pretty certain that only a limited number of units were set aside for pet owners at any of these resorts. Since rules tend to change all the time, consider that my information is a few years old. I haven't looked into pet friendly resorts in Branson for a long time.
I know you can eleminate Palace View, French Quarter, Grand Regency, Horizon's by Marriott (has recently changed it's name), Falls Village, and The Suite's at Fall Creek. None of those resorts allow pets.