Lullabye for a Stormy Night, by Vienna Teng.
Back to Pooh Corner by Kenny Loggins (google has it as ‘Return to Pooh Corner’ but I’ve never known it as such… weird).
And I third ‘Baby Mine’ and second Billy Joel’s ‘Lullaby.’
“Beautiful” and “Father and Daughter” by Paul Simon (off the Surprise cd)
“Daughter” by Loudon Wainwright (off the Knocked Up soundtrack)
Wonderful Baby by Don McLean
“Wonderful baby, livin’ on love
Sandman says maybe he’ll take you above
Up where the girls fly on ribbons and bows
Just laughin’ out loud and countin’ their toes”
Alll time best? This Woman’s Work, by Kate Bush.
It’s from a new father’s point of view, but I like Creed’s “With Arms Wide Open”:
“We stand in awe, we’ve created life
With arms wide open
Under the sunlight
Welcome to this place
I’ll show you everything
With arms wide open
Now everything has changed”
Well the obvious - “Wonder” by Natalie Merchant
“know this child will be gifted
with love, with patience
and with faith
she’ll make her way”
and Savage Garden’s “I knew I love you” usually thought of as a romantic love song, but my aunt tells me the song made her think of her pregnancy
“I knew I loved you before I met you
I think I dreamed you into life”
Faithless - To All New Arrivals I think fits the bill perfectly.
The whole album is great, but “A Kind of Peace” with Cat Power on vocals is such a beautiful song.
Amy Grant wrote “Baby Baby” for her daughter.
And Carly Simon’s “Love of My Life”
From the moment that I saw you
From the second that you were born
I knew that you were the love of my life
“Blessed” by Elton John (1995)
Also “I Love Being Pregnant at Christmas”*
I love being pregnant at Christmas
I feel like the round you virgin of yore
For though I have a warm bed to sleep in
There’s no room for me when I go to the store… 
*NOT by Elton John
Do they have to be nice songs? There’s “Doug’s Birthday Song” by Uncle Bonsai, which is all about giving birth, and foreshadowing of the life to come. (Sample here, lyrics here)
(Doug) Ten perfect little toes
(Doug) One perfect little nose
(Doug) Forgive the purple prose, they couldn’t have foreseen this
(Doug) Four perfect little limbs
(Doug) Three perfect little chins
(Doug) Two perfect earlobes, and a perfect little penis
Andrew Ratchin has been writing songs and singing for a couple decades, in groups and solo, returning often to the subject of Doug. Eventually there were enough songs for an album, called Doug. From Doug’s Birthday Song to Doug at the Gates of Hell, they’re a nice mix of funny and touching.
I sincerely hope not.
Mother’s Lament from Cream’s Disraeli Gears.
Stay Up Late by the Talking Heads is a good tongue in cheek song for new parents.