I'm learning about the different hero archetypes. As far as I know, Byronic heroes are charismatic, passionate, and flawed, among others. But can they be humorous? I can't think of any examples off of the top of my head from books or popular culture, so I'm not sure whether having a sense of humor fits that archetype.
The pure Byronic archetypical characters, such as Byron wrote, are noted for their sullen, defiant, arrogant, passionate, miserable, and withdrawn character. In particular, self-obsessed and lacking a sense of perspective -- which makes it difficult to see the humor in things.
It is possible to imagine leavening the character with a sense of humor, albeit a dark, sardonic one. However, even that much would result in a character that could be a Byronic hero but not an archetypical one. And too much would start to make him not one at all (though he might have commonalties).
Humor is a coping mechanism. Byronic heroes do not have good coping mechanisms.