I learnt the lullabye as "Baby's Boat" at Girl Scout Camp Bonnie Brea in East Otis, Massachusetts back in 1968, but the camp was already fifty years old at that point and all songs were strictly oral tradition. I hope this is close to what you remember. My kids have all loved it. It's a great tune.. hope you enjoy it with the grandkids.

BABY'S BOAT
(song writer unknown)

Baby's boat's a silver moon
Sailing o'er the sky
Sailing o'er a sea of sleep
As the clouds go bye

Chorus

Sail baby, sail
Out across the sea
Only don't forget to sail
Back again to me

Baby's fishing for a dream
Fishing near and far
His line a silver moon beam is
His bait a silver star