During the month of November, the Beehives set up a Beehive Babysitting service as one of their class activities. This allows parents to go out for an evening, get some Christmas shopping done, or for whatever reason.
The Beehives plan the whole thing, activities for the kids, even down to coordinating snacks. They have a sign-in board that the parents sign with a phone number, and who will be picking up the child.
The month before you can also hold a babysitting clinic to learn about proper babysitting skills, and even make a babysitting kit (box or bin full of things for kids to do).
This can also help them fulfill a Personal Progress requirement of offering service to others.
If you have lots of families with small children in the ward, you may want to pass around a sign-up sheet in Relief Society a week or two before, in order to limit the number of children to whatever the beehives can handle.