Strengthening the Oversight of Nuclear Nonproliferation Act of 2009 - Requires the President's Coordinator for the Prevention of Weapons of Mass Destruction Proliferation and Terrorism to report to the appropriate congressional committees: (1) annually regarding the Commission on the Prevention of Weapons of Mass Destruction Proliferation and Terrorism's findings concerning U.S. nuclear nonproliferation efforts; and (2) regarding U.S. cooperative efforts with the International Atomic Energy Agency (IAEA) on nuclear nonproliferation.