Checkpoint Safety Act of 2019 This bill revises minimum requirements for the deployment of armed law enforcement personnel at security screening locations at certain airports. Specifically, the Transportation Security Administration (TSA) must (1) order the deployment of at least one armed law enforcement officer within 300 feet of the security screening location and within the terminal during operating hours of each airport having annual enplanements of 8 million or more or international enplanements of 1 million or more, and (2) order the deployment of additional armed law enforcement officers at such airports if necessary to ensure airport security. The bill modifies air transportation security program requirements to include ensuring high training standards for all security and law enforcement personnel, and multiple means for the TSA or members of the public to request prompt law enforcement assistance in the airport. The bill eliminates the TSA authority for allowing deputized state and local law enforcement officers to be stationed other than at airport security screening locations.