Mark Meritt has a wonderful webpage with lots and lots of resources for both piano teachers and students. One of those resources he has made freely available is Accompaniments. Right now, because of the holiday season, he has made available a 2 page pdf file of Christmas songs in the key of C, plus instructions on how to know when the downbeat occurs. That's a huge help in knowing when to change to the next chord.
Go to his "Accompaniments" page for additional links to a comprehensive list of fake books available, and other student/teacher resources.