To file your return, please see Carl's guidance at How can I claim child care credit with no EIN or social?
If you can't provide the Child Care Provider's Social Security Number or Employer Identification Number, you have to, at a minimum, show due diligence that you've attempted to get one of those identifying numbers. The IRS is adamant about this. And, without the provider's identifying number, you can't e-file your return -- it will be rejected by the IRS -- and you'll need to file your return on paper and mail it in.
Seen page 9 of IRS Publication 503, Child and Dependent Care Expenses for more information.