Small Airport Relief Act of 2003 - Amends the Aviation and Transportation Security Act to extend through FY 2004 the part of the formula for apportionment of airport improvement program funds under which the Secretary of Transportation shall use, in lieu of passenger boardings at an airport during the prior calendar year, the greater of: (1) the number of passenger boardings at that airport during 2000; or (2) the number of passenger boardings at that airport during 2001.