I'm not saying this was the original tune, but if you want to sing these words anew, you can use the traditional melody to 'The Happy Christmas Comes Once More.' Another set of words to the same tune is 'The Bells of Christmas.'

Here's the URL for a YouTube video where it is played on an organ.

https://www.youtube.com/watch?v=jLN5GhE6ZZo

Who knows? To me, the words fit so well that that may have been the tune used for 'The Christmas Bells.'