Peter said, "I saw a movie yesterday."
In reported speech, should I use 'the day before' or 'the previous day' to replace 'yesterday'?
Peter said that he had seen a movie the previous day / the day before.
I would use "Peter said [that] he had seen a movie the previous day" but there is nothing wrong with "the day before".
Remember - if you don't use correct capitalisation, punctuation and spacing, anything you write will be incorrect.