Preventing the Spread of Nuclear Weapons Act of 2019 This bill requires the President to obtain congressional approval before entering into or renewing a nuclear cooperation agreement with a foreign country in certain cases. Before entering into or renewing such an agreement, the President shall report to Congress on (1) any credible evidence that the foreign country intends to pursue a nuclear program that is not inherently peaceful; and (2) any instance where the country has violated international standards related to weapons of mass destruction, including certain treaties relating to nuclear and chemical weapons. If the report contains any such credible evidence or instances, the President may not enter into or renew the treaty unless (1) the President submits a proposed agreement with the foreign country that meets specified statutory requirements related to nuclear cooperation agreements, and (2) Congress passes a joint resolution approving the agreement. These provisions requiring a proposed agreement and congressional approval do not apply if the foreign country is a member of the North Atlantic Treaty Organization (NATO) and a nuclear weapon state.