Any approach I can think of would likely not appeal to some people, or not work for every site.
One idea could be to grey off the faivicon. Which assumes the site's favicon isn't already B&W or greyscale...
Another could be to replace the favicon with a small "zzz" icon. Which is perhaps quite ugly?
I imagine for some users, this will be a big issue, whereas for others they will not care and won't want the visual change. If there's enough space, a "zzz" could be added to the right hand side of the tab icon, but that's maybe not as minimal and elegant as would be ideal.