Yes, child care expenses paid to a family member are eligible for the Child and Dependent Care tax credit if the family member isn't your spouse, the parent of your qualifying child, or your dependent, and you meet all the tests to claim the Child and Dependent Care Credit. Your family member will be responsible for reporting the child care income on their own tax return.
If your child (including stepchild or foster child) provided the care, he or she must have been age 19 or older by the end of the year, and he or she can't be your dependent.
Read more here about the child and dependent care credit on the IRS website.