There are only a few moments where we can see Michael smiling:
- "Do you like your Lasagne?"
- "Then would you like me better if I were Ingrid Bergman?"
- The deleted bed scene between Michael and Kay.
- Michael sees Appollonia touching his gift.
- Michael teaching Appollonia how to drive. (Which is kind of funny because Al Pacino didn't have a driving license back then.)
If I remember correctly he smiles twice at Anthony's party: Once when the photo with the cheque is taken (a fake smile). And in the deleted scene with Sonny's daughter.

The reason why is smile disappears is simple: The Godfather Trilogy is the story of Michael's tragedy. A man who sacrifices all his hopes, all his love for the sake of what he thinks is "his family", which in fact is a crime organisation. In GFII, he finally destroys his family, believing, he's protecting them.