The marionette motif makes at least three appearances in the films:

In GF II Fanucci watches a street performer putting on a marionette show ("Oh.....this is too violent for me")

Also in II, there's a scene where Michael, Kay, and Anothony are in their car, and Anthony is playing with a marionette; a little bird I think it was. You have to watch closely, though, 'cause it's easy to miss.

And in III, there's a scene in Corleone, Sicily, where Michael and Kay also watch a street performer doing a marionette show.