Is the cost of tuition for a Certified Nursing Assistant training course tax-deductible? We did pay tuition to the school for the course, but did not receive a 1098-T.

Yes, if your student attended an eligible education institution, the course will qualify and your student should receive a 1098-T.  (It may not yet be available or it may only be available online, so check with your school.)

An eligible educational institution is a school offering higher education beyond high school. It is any college, university, trade school, or other post secondary educational institution eligible to participate in a student aid program run by the U.S. Department of Education.

This includes most accredited post-secondary schools.

If you aren’t sure if your school is an eligible educational institution, ask them.