1570s, "full of corn, pertaining to corn," from corn (n.1) + -y (2). Chaucer used it of ale (late 14c.), perhaps to mean "malty." American English slang "old-fashioned, sentimental" is from 1932 (first attested in "Melody Maker"), perhaps originally "something appealing to country folk" (corn-fed in the same sense is attested from 1929). Related: Cornily; corniness.
There's an element of truth in every idea that lasts long enough to be called corny. [songwriter Irving Berlin (1888-1989), in a 1962 interview]