I'm not sure when you can start to make reservations. My guess is six months out, like the dining. So now?
From Page 1 (Ameneties Section):
Kids Programs
Sandcastle Club
Hours: 4:30 PM to 12 midnight
Reservations: (407) WDW-DINE
Designed especially for children ages 4-12 years old.
Supervised activities including free play arcade games, Sega/Nintendo, board games, Disney movies), "play" kitchen and living room area, dolls and stuffed animals, arts and crafts, and much more!! Charge is approximately $12 USD per hour per child, with a two-hour minimum. Sandcastle Club provides a complimentary dinner for children that is available at 6:00 PM, 7:00 PM and 8:00 PM in the Club. Reservations required.
Visit the Sandcastle Open House each day from 1 PM to 3 PM for a variety of video games, toys and arts and crafts. Fun for the whole family!
Kid's Nite Out, Inc.
Kid's Nite Out caregivers can provide one-on-one in-room childcare in the comfort of a Walt Disney World® Resort room. The professional staff of Kid's Nite Out gives the child individual attention by playing a variety of fun-filled activities with him/her including reading books, coloring, or playing "I Spy" games. They can also provide a fun, well-trained sitter to just hang out with the family if they need a father's/mother's helper. Kid's Nite Out also plans and works children's parties, camps, and children's theme conventions.