Southwest Border Violence Reduction Act of 2009 - Directs the Attorney General to: (1) to expand resources for the Project Gunrunner initiative of the Bureau of Alcohol, Tobacco, Firearms, and Explosives (ATF) to identify, investigate, and prosecute firearms trafficking across the U.S.- Mexico border; and (2) provide ATF agents, equipment, and training to assist Mexican law enforcement officers in combating firearms trafficking and other criminal enterprises.