Not Barney, and especially not the Wiggles.
I mean songs that real songwriters wrote for their kids. Forever Young by Bob Dylan* would be the premier example.
The kids have every verse of Forever Young memorized, and I need something else to put them to bed with.
*But not him singing it. 
Billy Joel has “Good Night My Angel”
Of course “Hey Jude” for Julian Lennon
I don’t know who it was written to, but Mary Chapin Carpenter’s “Dreamland” is nice.
Loudon Wainwright III’s “Lullaby” references his son Rufus but it may not be what you’re looking for!:
*The excuse that you’re crazy is useless
You’re not biting you’re barking you’re toothless
But you’re ruthless (you’re Rufus)
Shut up and count some sheep
And do me a favour don’t bitch in your sleep
No more agony please no more sorrow
Shut up and catch some Z’s*
Was **Yellow Submarine ** originally written as a children’s song?
Ben Folds has different-sex twins, and wrote “Still Fighting It” for his son and “Gracie” for his daughter. Both beautiful!
Loudon also has “Rufus Is A Tit Man” and “5 Years Old” for Rufus and Martha respectively.
And Lucy in the Sky with Diamonds about a Beatle kid’s artwork.
Back to Pooh Corner by Kenny Loggins.
The Rainbow Connection by Kermit.
Tom Chapin, Harry’s more talented brother, has a series of great children’s songs that are just as much fun for adults. His stuff is clever, humorous, sophisiticated and often quite sweet without ever becoming cloying. “Family Tree” is a good place to start.
And you might be interested in Rockabye Baby Records, with lullaby renditions of songs by Metallica, Radiohead and more!
Bill Staines “The Happy Wanderer” CD.
I listen to it when I travel.
St. Judy’s Comet by Paul Simon is a lovely lullaby written for his son. In addition, Loves Me Like A Rock and Mother and Child Reunion are also evocative of the bond between a mother and child.
Billy Joel also has a lullaby (presumably to his daughter) called Lullabye (Goodnight, My Angel).
Beautiful Boy (Darling Boy) by John Lennon was written to and about his son, Sean, who was then 4 years old. (It ends with him whispering “Good night, Sean… I’ll see you in the morning”, and he recorded it just a few months before his murder :()
Will Smith recorded a song called Just The Two Of Us about and to his son that heavily sampled the song of the same name by Grover Washington and Bill Withers.
Neil Young has a song Sugar Mountain which is about growing up and leaving youth behind. (Oh, to live on Sugar Mountain, / With the barkers and the colored balloons… / You can’t be twenty on Sugar Mountain / Though you’re thinking that you’re leaving there too soon…)
Eminem had a recent hit called Mockingbird written to his daughter, Hailie (though it is rather dark).
On an even more depressing note, Eric Clapton’s song Tears In Heaven is a song addressed to (in the second person) his four-year-old son who fell to his death out of a window of a high-rise apartment building in a freak accident.
On the other hand, Sweet Child O’ Mine by Guns ‘n’ Roses is not a song to a child, but could be
The Cape by Guy Clark and Katie Belle by Townes van Zandt can both be found on the album Together at the Bluebird Cafe.
Dar Williams’ “So Close to my Heart” is dedicated to her son.
I would recommend just about anything by Trout Fishing In America. It’s kids’ music that doesn’t irritate most adults. Ditto for Peter, Paul & Mary. Someone mentioned both Paul Simon’s song St. Judy’s Comet and Kenny Loggins’s Pooh Corner – Loggins has an album (Return to Pooh Corner) that includes both these songs, and a bunch of other kid-friendly songs like The Rainbow Connection, All The Pretty Little Ponies and Too-Ra-Loo-Ra.
Checking on Amazon, I see there’s also “More Songs From Pooh Corner” and there’s a bunch of other recommendations in their “people who bought this also bought” thingie.
You might also look for Songs For Our Children - pop artists recorded children’s songs to benefit the Pediatric AIDS Foundation.
My favorite is Taj Mahal’s cd Shake Sugaree. It’s got Fishin’ Blues, Brown Girl in the Ring, Funky-Bluesy ABC’s, A Soulful Tune, and lots of others.
(Sorry, pressed enter too soon.)
From the time they were babies, I’d hold them while dancing to Brown Girl in the Ring, then stop moving suddenly when the music stopped in the middle, then start again. It got gleeful giggles from them everytime.
There’s also an album that Jerry Garcia and David Grisman recorded called “Not For Kids Only.”
Dan Zanes. I can listen to his band all day.
One word: No!
Perfect! …my kids have played “Jerry or Bobby”…and sometime have played “Jerry or Dave”, for years…they are now 18 and almost 16…
It is a great album, or should I say CD.
Peace, love and jerry…
tsfr