Aircraft with a standard airworthiness certificate that meet the specifications listed below may be flown by sport pilots. However, the aircraft must remain in standard category and cannot be changed to light-sport aircraft category. Holders of a sport pilot certificate may fly an aircraft with a standard airworthiness certificate if it meets the definition of a light-sport aircraft.
Some models of the classic and nostalgic airplanes such as the Piper Cub, Aeronca, Ercoupe, Interstate, Luscombe, and Taylorcraft meet the criteria of a LSA and may be flown by sport pilots.
For a list from the FAA of the specific models of existing standard category aircraft that meet LSA criteria go to: FAA LSA: Existing Type Certificated Category (download .pdf).