Introducing TennCare’s Diaper Benefit! TennCare now provides up to 100 diapers per month for TennCare and CoverKids children under age two. Visit our pharmacy and present your child’s pharmacy card. If your newborn doesn’t have a card yet, you can use the mother’s pharmacy card or Social Security number.No prescription is required. At this time we cannot guarantee specific brands, as suppliers are having issues getting them to us and other pharmacies. Fill out the request form by Clicking HERE: We will also have this form available to fill out at the pharmacy