In some employment there is a shift differential meaning those working second or third shift get paid slightly more than those on day shifts but for those working 12 hour shifts not as much as it balances out over a 2-4 week period. One issue is not everyone works consistently nights and has some day shifts which you wouldn't be able to accommodate if you already your kids for daytime. But there is for sure a demand for this kind of thing.

If you live near a college or university there will be students needing till midnight to attend night classes as compared to overnight. Although you will be giving two meals you will only be giving one snack or something small before bed. In contrast you won't have the craft expenses of a day program as there will only be a couple hours before the children go to bed which can be used for freeplay, stories, etc. I would probably take your daytime rate and add a $5 shift premium to it. Take into consideration the children are sleeping.