Assuming he meets all the qualifications that your older child did, he would be eligible. Go over your answers for the first child (including those under dependency in Personal Info), see how you answered them, and verify that you answered both sets exactly the same. It is easy to miss something.
Remember, your child must have lived with you for over half the tax year and that the credit is based on the first $6000 of expenses, regardless of how many children you claimed. If you spent that amount on one child, you have exhausted the credit limit.
See below for all the qualifications:
To qualify for this credit, you must meet all of these criteria:
- You (and your spouse, if filing jointly) must have earned income
- The earned income requirement for one spouse is waived if s/he was a full-time student or
- Disabled, if they lived with the other spouse for more than 6 months in 2019
- You paid caregiving expenses so that you (and your spouse, if filing jointly) could work or look for work
- The work/look for work requirement for one spouse is waived if s/he was a full-time student or
- Disabled, if they lived with the other spouse for more than 6 months in 2016
- You paid a caregiver to care for a Qualifying Person. The caregiver cannot be:
- Your spouse;
- Your dependent;
- Your child if they were under 19 on the last day of 2019, even if not your dependent; or
- The parent of the Qualifying Person, if the Qualifying Person is your child under the age of 13 during 2019.
- You cannot file with the Married Filing Separately filing status
- You must furnish the care provider's name, address, and (unless it's a tax-exempt organization) their SSN, ITIN, or EIN on your return.
From <https://ttlc.intuit.com/questions/1900643-what-is-the-child-and-dependent-care-credit>
