Certainly sunspots (or "starspots") won't count, as they are statistically random and thus unpredictable, as well as causing a very small delta in total output.
I stand corrected. There's a Wikipedia page (thanks, HDE) which describes several classes of aperiodic stars. These stars do continue to undergo significant variation for at least many days, apparently.
The wiki page on general(periodic) variable stars identifies two classes:
This variation may be caused by a change in emitted light or by
something partly blocking the light, so variable stars are classified
Intrinsic variables, whose luminosity actually changes; for example,
because the star periodically swells and shrinks.
whose apparent changes in brightness are due to changes in the amount
of their light that can reach Earth; for example, because the star has
an orbiting companion that sometimes eclipses it. Many, possibly most,
stars have at least some variation in luminosity: the energy output of
our Sun, for example, varies by about 0.1% over an 11-year solar
After that, one descends into pulsars, binary stars, Cepheids, and lots more.