There are babysitting services, I don't have any experience with those though.
If you are staying at the GCH, they offer a place that you can drop the kids off while the adults enjoy an evening out. This is taken off of the website:
Pinocchio's Workshop
Enjoy a night out and treat children ages 5-12 to an evening of arts and crafts, computer games, Disney films, dinner and snacks with a caring, licensed supervisor in an environment created for them (available to Resort Hotel Guests; additional fee).
Our kids really wanted to do this years ago, but at the time my youngest son wasn't old enough. It looked like a fun place for the kids to hang out though.