Biogas Production Incentive Act of 2009 - Amends the Internal Revenue Code to allow a business tax credit for the production, sale, or use of biogas. Defines "biogas" as a gas that is derived by processing qualified energy feedstock (i.e., manure of agricultural livestock and other organic agricultural or food industry byproduct waste material) in an anaerobic digester and that contains at least 50% methane. Allows such credit to offset alternative minimum tax (AMT) liability.