If anyone can name this old carol and maybe provide the complete lyrics, I'd appreciate it.

"Shoon-a-shoon, I sing no psalm, little man,
Although I am out of David's House and clan.
Shoon-a-shoon, I sing no psalm...

Hush-a-hoo, whirring of wings...
Hush-a-hoo, stirring of strings...

Though in slumber deep,
His ear can hear my song of sleep."

It has to be Irish, but it has a distinctly Hebraic melody. Always sort of felt as if it went with "O Come, Emmanuel".