My sister, who is 12 years older than I am and more like my mother, sang me to sleep with that song as long as I can remember. It makes me feel like a small child when I hear that song.
I sang "Daddy's Little Girl" and changed the words to "Mommy's little boy" for my boys, You are My Sunshine, Jesus Loves Me, and sometimes I just hummed. I had one son that I had to sing "As the Deer" to - he would say, "Pantin for, Mama." It makes me miss him to think about it, now that he's grown and far away.