Starliner was the fastback roofed version of the Galaxie produced in 1960-61. Biggest engine available was 390, up to 401 horsepower with a tripower in 1961. Here are some pics of my old one...http://www.gt350h.com/galaxies/galaxies.html. Sunliner was Ford's model name for convertibles from the mid fifties until 1962. A 1962 Sunliner could be had with a 405 Horsepower 406 tripower.
The guy saying the 427 appeared in 1963 in the fastback roofed Galaxie Starliner is correct. In 1962, the offering was a 406 ci engine. I remember these well because I wanted one bad. I finally afforded my first muscle car in 1965 but it was a Chevelle SS396 (the big cube Starliner was no longer offered). Sunliner was the name given to convertibles. Starliner was the name given to hardtops with slanted rooflines.
My brother had a '61 Sunliner with a dual-quad 427, but it was a transplant. The big engine that year, as someone else has already noted, was the 406. What a car that was! Thanks for the memory. /forums/images/icons/smile.gif