A few years ago, we were able to reserve the Neverland Club (at the Poly) for our three kids ahead of time, by calling Disney Dining 407-WDW-DINE. They had a minimum and the price included a kid-friendly supper buffet at that time. There was also a slight discount for the 2nd/3rd/4th child in a family.
Offsite, there are Kids Night Out arrangements at many of the larger timeshare resorts (3-4 hours, crafts, games, pizza, movie). Marriott Cypress Harbour, Marriott Grande Vista, Vistana Resort, and Orange Lake Country Club all come to mind. Prices are slightly lower than Disney's, perhaps $20-$25 per child for the evening. These are for registered guests only and usually require 24 hours advance reservation. IIRC, someone may have posted that HIFS also offered this.