Technically speaking. Genjutsu shouldn't work on the Six Paths of Pein. Not speaking about Nagato, just the corpses he uses.
The main reason for this is the nature of genjutsu and how the different bodies work.
Genjutsu disrupts the targets chakra and five senses to pull them into an illusion.
All of the Peins' are corpses that get chakra sent to them, and with that if you were to put any single path into a genjutsu another path could see this and that would alert Nagato. Nagato would then stop sending chakra (Disrupting his own chakra system and allowing the body to escape the genjutsu).
The chances of catching all of the bodies in a genjutsu is pretty. . Unbelievable. And techniques like tsukuyomi would effect the paths, not Nagato himself. And again, if a few paths see several different events going on Nagato could disrupt or stop sending chakra for a few seconds. Which would break them out of the genjutsu.
So really, genjutsu shouldn't work on Pein. The chakra rods/receivers make him extremely immune to it. So, unless you're fighting a single path or two. . . And a fairly proficient genjutsu user. . . You probably won't catch him in a genjutsu for too long, if you even manage to get him in one.
I'd say his weakness would be fighting an enemy with intel and rivaling power. Such as Sage Mode Naruto.