Please justify the title A Christmas Carol.

In order to justify the title, I think we need to look at the definition of a "carol."  The Webster's dictionary site defines this as

• a song of joy


• a ballad of religious joy

Given this definition, I think that the title is appropriate to this book.

The book is a song of joy (and possibly of religious joy) because it follows Scrooge as he changes from being an unhappy and selfish person to being a happy and generous one.  Scrooge ends up as a happier person and that in itself is joyful.  It is religious because Scrooge's changes bring him more into line with what a Christian is supposed to act like, especially at Christmas.