Help! Christmas songs / carols

Evening,

just had a very random request. Someone is entering a little competition and needs to know a couple of answers. The quiz is christmas songs or carols. They give you the initials, you've got to work it out. Out of 50, she just needs 2 more. The inititials that's stumped her are:

M.C.B

&

I.D.J

For example IBIFC was I believe in father Christmas. If any of you research whizzes can help, it would be much appreciated.

Actually I made a typo. It was MBC - Mary's boy child. As for the other one.... thanks Stressy! You're a star!.