Social Security Caregiver Credit Act of 2019 This bill credits certain individuals who provide at least 80 hours of care per month to dependent relatives without monetary compensation with up to five years of deemed wages (determined by a specified formula) for purposes of determining Old-Age, Survivors, and Disability Insurance benefits. However, this requirement shall not apply if a larger benefit or payment would otherwise be payable. The bill also authorizes the Department of Health and Human Services to make grants to support state programs that provide medical training to individuals who provide care to dependent relatives without monetary compensation.