He needs that eye to use this genjutsu.
So far, Infinite Tsukuyomi is the strongest genjutsu, so it's understandable that Madara needs the Rinne-Sharingan + the power of a god.
Again, I think it's nonsensical to believe Madara can use such a powerful genjutsu but he is incapable of using a much weaker genjutsu like that.
Unlike Kagatsuchi, KA or Kamui, Amaterasu and Tsukuyomi weren't shown to be pure exclusive MS jutsus for a particular user. The fact that two brothers had it support my argument.