Sway with me in the tops of the trees

My mom used to sing me to sleep with this lullaby. I don't know where else it's from, and can't find anything close to it on the internet. It probably has a different title too.

Partial Lyrics:
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...the man in the moon
is climbing the sky...

...
it says "come with me,
come sway with me
sway with me
in the tops of the trees"
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