§24(h)(4) does allow the partial credit to be claimed so long as the dependent is a resident of the US.  Although the conference report and blue book both indicate the Congressional intent to require an ITIN, this requirement has not yet been codified and will necessitate a technical correction.

If PS is not computing the credit as expected, you may want to check that you have chosen "son" or "daughter" instead of "child" for relationship or vice versa.  I use PTO and found that the credit is not computed when "child" is chosen and this triggers a critical diagnostic that the relationship is invalid but without reference to the partial credit.  Once the change is made, PTO would then compute the credit correctly.