Try this for non citizen SSN info

http://www.ssa.gov/pubs/10096.html#immigration

The child should be a qualifying child (#5)

http://www.irs.gov/pub/irs-pdf/p972.pdf


EDIT:

Forget the above. You must have SSN to claim the credit.


Internal Revenue Code Section on the Child care credit.

6428(h) IDENTIFICATION NUMBER REQUIREMENT. --



6428(h)(1) IN GENERAL. --No credit shall be allowed under subsection (a) to an eligible individual who does not include on the return of tax for the taxable year --



6428(h)(1)(A) such individual's valid identification number,



6428(h)(1)(B) in the case of a joint return, the valid identification number of such individual's spouse, and



6428(h)(1)(C) in the case of any qualifying child taken into account under subsection (b)(1)(B), the valid identification number of such qualifying child.



6428(h)(2) VALID IDENTIFICATION NUMBER. --For purposes of paragraph (1), the term "valid identification number" means a social security number issued to an individual by the Social Security Administration. Such term shall not include a TIN issued by the Internal Revenue Service.

6428(h)(3) SPECIAL RULE FOR MEMBERS OF THE ARMED FORCES. --Paragraph (1) shall not apply to a joint return where at least 1 spouse was a member of the Armed Forces of the United States at any time during the taxable year.

you will have to get one to claim the credit.