I think that's a great idea! To email the parents and let them know that you're sick and you are open for those who are desperately in need of care only. Let them know the kids have a free play day. It would encourage some to keep them home without you feeling the guilt of sending them all away.

Knock on wood... I've only been sick enough to close once and it just happened to be a day when I only had one child.

I hope you feel better soon!