The term "super-hero" is certainly older than Superman. In fact, some etymologies place it as being older than the 20th Century.
Like with many phrases that begin with "Super-" superhero may be a German imported term (including "Superman," which was used in German as far back as 1527).
I suspect the recent origin and use may be related to Smith & Sons.
Smith & Sons used the term "super-hero" pre-Superman in house advertisements for the Shadow and Doc Savage pulp magazines. It should be noted that nowhere in the 182 Doc Savage novels is the Man of Bronze ever explicitly CALLED a superhero, of course...but he was called so elsewhere. For instance, when Doc Savage first came to radio in 1934, this advertisement played:
"That superhero, Doc Savage, comes to West Coast radio-listeners each Sunday night at 9 p.m. over the Don Lee California network, sponsored by Cystex, the Knox Company product." [/list]
The December, 1935 issue of the Shadow has this advertisement:
FULL LENGTH NOVELS OF THE EXPLOITS OF THOSE TWO GREAT SUPER-HEROES OF MODERN FICTION--DOC SAVAGE AND THE SHADOW" [/list]
Also, Walter Gibson, author of many Shadow novels used the term "Super-" to refer to anything weird, out of the ordinary, and to underscore the prounounced qualities: "supercrime" (which goes back to Gibson's 1932 Shadow novel, DEAD MEN LIVE).
And it should also be noted that in common use, the prefix "super-" was widely used considerably prior to the period we're talking about; for instance, "Supermarket" is a term that goes back to the 1920s. In the first appearance of the Simon/Kirby Guardian in 1942, the Guardian is called a "super-hero." The point here is that for such a term to be used right away without explanation in a magazine for children implies that it must be considerably more established.
One of the reasons that "super-hero" feels like a recent term (I've seen some fans wonder if it even existed before ADVENTURE COMICS #247, with the Legion of "Super-Heroes" first appearance) is that Roy Thomas in a lot of his period work ALL-STAR SQUADRON, et. al., chose to use the more period-evocative term "Mystery Man."