Per IRS Instructions for Form 2441 Child and Dependent Care Expenses, on page 3:
If the care provider is an individual, enter his or her SSN. Otherwise, enter the provider's employer identification number (EIN). If the provider is a tax-exempt organization, enter “Tax-Exempt” in column (c).
U.S. citizens and resident aliens living abroad. If you are living abroad, your care provider may not have, and may not be required to get, a U.S. taxpayer identification number (for example, an SSN or EIN). If so, enter “LAFCP” (Living Abroad Foreign Care Provider) in the space for the care provider's taxpayer identification number.
Returns can be e-filed even if the care provider was a tax-exempt organization with no EIN. When going through the Q&A interview screens for company or organization Child and Dependent Care Providers, you can check The organization is a non-profit and does not have an EIN. Per the instructions, "Tax-Exempt" will print on Form 2441, Line 1, Column (c).
For an individual care provider, a social security number is needed for e-filing. If your care provider is foreign and does not have or is not required to have a taxpayer identification number, you can check This is a foreign provider that is not required to get a U.S. identification number. Per the instructions, "LAFCP" will print on Form 2441, Line 1, Column (c).
Note that any link in the information above is updated each year automatically and will take you to the most recent version of the document at the time it is accessed.