Of course the Magi/Kings are likely to figure to some degree in most Innocents' Day carols. A case in point being my own "In Bethlem Town", to the PESKY SARPENT tune ("On Springfield Mountain there did dwell"); they are in vv. 4 & 5:

1. In Bethlem town the Christ was born.
   They laid him down that starlit mor-ee-orn
   Amidst the corn, in swaddling gown
   Unbleached and worn, with hay his crown.
   Too-loo-ree-loo, too-loo-ree-lay,
   Too-loo-ree-loo: 'twas Christmas Day.


2. On hills nearby, poor shepherds graze
   Their flocks. The sky explodes in prai-ee-aise,
   With angels' lays to God on high:
   "Fear not, this day salvation's nigh!
   Too-loo-ree-loo, too-loo-ree-lirth,
   Good will to you, and peace on earth!"


3. The shepherds then of one accord
   To Bethlem ran to greet the Lor-ee-ord.
   They found him sleeping in a trough,
   Convolved in cheap, unwhitened cloth.
   Too-loo-ree-laid, too-loo-ree-lotched,
   They knelt and prayed as Mary watched.


4. From Persia far, wise Parsees came,
   Led by his star, to praise his name-ee-ame.
   They brought presents of gold and myrrh
   And frankincense--and beaver fur,
   Too-loo-ree-lurr, too-loo-ree-lee,
   Then went home sur-reptitiously.


5. King Herod had bequestioned them,
   With motive bad, about Bethlem-ee-em.
   The crafty sages Herod left
   In royal rage, of facts bereft--
   Too-loo-ree-lilled, too-loo-ree-lents,
   So Herod killed the Innocents.


6. God said to Joseph and his wife:
   To Egypt go, to save your li-ee-ife.
   Thine ancient namesake as a slave
   To Egypt came your folk to save.
   Too-loo-ree-lask, too-loo-ree-lun,
   A sim'lar task awaits your son.


7. Good people all, consider ye,
   Whom God hath called to liberty-I-ee--
   Consider well the awful cost
   The Scriptures tell in children lost;
   Too-loo-ree-low, too-loo-ree-laid,
   Consider now the ransoms paid.


8. God's peace to you; now merry be,
   For 'tis all true, of verity-I-ee.
   The baby born, ye know it well,
   That holy morn, hath vanquished Hell,
   Too-loo-ree-loss, too-loo-ree-lee,
   Upon the cross, and we are free!