My mom used to sing "You are my sunshine" to us...not sure if it's exactly a lullaby, but it's soft so it works. I have the feeling I'm going to be singing it a lot to my little sunshine. :)
I sing wonderwall by Ryan Adams lol that or hush little baby
I hum songs sometimes to my baby...I think that sounds more like what they hear in the womb. I like twinkle twinkle little star. There was a song I made up for my oldest daughter who is now 21, she had colic and later some issues going to sleep at night so I would sing this song to her very slow and in a very soft voice.
Close your eyes and go to sleep
In the morning when you wake up
We might go outside
We might go outside, and catch a butterfly
We might see a little bird...
Lol I know it's not going to make the number one on the charts but I just made it up and for some reason it calmed her and she would go to sleep.
I didn't sing a lullaby really just "Close to you" by Karen Carpenter. My daughter has always loved it and still asks me to sing it to her if she is upset. I think any song that seems special to you and is calm and soothing will do. Making them up is great too. They just like to hear the sound of your voice.