* "The Holly and the Ivy": This carol is believed to be of medieval origin, dating back to the 15th century. The lyrics are simple and depict the holly and ivy as symbols of Christmas. The line "Christmas is a-coming, the King of Heaven shall be born" is a key part of the carol.
* "I Saw Three Ships": This carol is also very old, possibly dating back to the 16th century. It tells the story of the three wise men traveling to see the newborn baby Jesus. The line "Christmas is a-coming, let us be merry and bright" is a common refrain in this carol.
* "The Twelve Days of Christmas": This carol, while originally a children's song, has the line "Christmas is a-coming, and the bells are ringing" in some versions.
While these are the most well-known, other carols use similar variations of the phrase. Therefore, there's no single author credited with writing "Christmas is a-coming". It's a common expression that has evolved throughout history, being adapted and incorporated into various Christmas carols.