You do not need to issue any 1099 form at all since this was a personal expense and you are not a business with an EIN.
All you need to do is enter their name, address and SS# on the form 2441 (included in your tax return) which serves the same purpose as the 1099 forms.
FYI ... the form 2441 was originally put into service for just this very situation ... to catch all the "home day care providers" that were not reporting the income on a tax return. By giving a credit to the parents they got them to "report/turn in" the day care provider so the IRS will be looking to their tax return for the amount you paid them (on the 2441) to show up as income on their tax return. It is just that simple ... don't even try to do any 1099 forms at all.
