I'm just focusing on game completion %age at the moment so I'm just about to do the lightweight cup... where the only stipulation is 3400mm length or less O_o. Anyway, I can't seem to find a car that isn't pre 70's
Try searching for "lightweight" in thread titles on the GT4 board (and child forums), and see what you get. Odds are that somebody has asked this before, or at least done a race report of it.
My notes are confused, but I used either the Abarth A112, or a Suzuki Cappucino.