I don't see how an entire genre can consist of only one real character, and remain meaningful.
Well, subgenre, and if anyone could do it, it would be Conan. But you're right, I guess. Howard did do some other very good characters within the Genre. Bran Mak Morn and King Kull come to mind. And Fahfrd/GMouser is very close to Conan, while being very different