Actually, I think the song list is kind of meager so far. "Hark the Herald Angels Sing" is the best one so far, because it actually has a distinct gospel message. In fact, as far as hymns are concerned, some of the best gospel messages can be found in the Christmas hymns.
Drop "Away in a manger." Here's why: if you've ever heard the words or sang them yourself, you know that it is a fairly inaccurate description of what probably actually happened on Christmas. "The little Lord Jesus, no crying he makes?" Come on, he was a baby. He's gonna be screaming and pooping just like every other baby boy. As much as that song presents the first Noel as one of the gentlest nights in history, i believe that the night Christ was born was a very tumultuous night. Obviously, if there was no room for them in the Inn, there was plenty of busyness. Anything that mentions that Joseph and Mary found a stable outside of harm's way to give birth to Jesus would have probably been very inaccurate. I think they found a manger just outside of "the Inn," probably in an alley behind it, where people from the Inn were keeping their horses. It's good to remember that the world Jesus was born into was not a clean one. There was literally crap everywhere, a perfect metaphor for the hearts of man.
Drop "We Three Kings." Nowhere in the Bible does it mention that there were 3 kings... or even 3 wise men. It mentions "wise men" coming from the East, and it briefly mentions the kinds of gifts they brought the young Jesus. Because only three specific gifts were mentioned, the writer of this song along with many MANY other people felt that it stood to reason that there were only three actual men there...
I think you all probably have heard all this before. I don't mean to throw "that's not what the Bible says" stuff at you... I just think we could look for more conventional hymns of Christ's birth to sing:
"O come, O come Emmanuel, and Ransom Captive Israel,
who mourns in lowly exile here until the Son of God appear.
Rejoice! Rejoice! Emmanuel shall come to thee, O Israel."
"O holy Child of Bethlehem, descend to us we pray.
Cast out our sin, and enter in. Be born in us today.
We hear the Christmas angels the great glad tidings tell;
O come to us, abide with us, our Lord, Emmanuel!"
"Fall on your knees! O hear the Angels' voices!
O night divine! O night when Christ was born!"