Supply Our Soldiers Act of 2009 - Directs the Secretary of Defense to provide for a program under which postal benefits are provided to a member of the Armed Forces who is on active duty and who is either: (1) serving in Iraq or Afghanistan; or (2) hospitalized at a military medical facility as a result of such service. Provides the postal benefits in the form of coupons or other evidence of credit (vouchers) to use for postal-free mailings.