Jerry played this a few times with David Grisman in 1991-92, and long before that with the Sleepy Hollow Hog Stompers in 1962. The lyrics from the Garcia/Grisman versions are:
Peaches in the summertime
Apples in the fall
If I can't get the girl I love
I don't want none at all (note 1)
Chorus
Shady grove, my little love
Shady grove, I know
Shady grove, my little love
I'm bound for shady grove
Wish I had a banjo string
Made of golden twine
Every tune I'd play on it (note 2)
I wish that girl were mine
[chorus]
Wish I had a needle and thread (note 3)
Fine as I could sew
I'd sew that pretty girl to my side
And down the road I'd go
[chorus]
Some come here to fiddle and dance
Sme come here to tarry
Some come here to fiddle and dance
I come here to marry
[chorus]
Every night when I go home (note 4)
My wife, I try to please her
The more I try, the worse she gets
Damned if I don't leave her
[chorus]
Fly around, my pretty little miss (note 5)
Fly around, my Daisy
Fly around, my pretty little miss
Nearly drive me crazy
[chorus]
Notes
(1) on the "Pizza Tapes", Jerry sings "I won't have none at all"
(2) on the "Pizza Tapes", Jerry sings "Every tune I'd pick on it"
(3) Jerry doesn't sing this verse on the "Pizza Tapes"
(4) Jerry sings this verse twice on the "Pizza Tapes"
(5) Jerry sings this verse on the "Pizza Tapes" but not on the version on "Shady Grove"
The lyrics Jerry sang in 1962 were (thank to Matt Schofield for the transcription):
Chorus
Shady grove, my true love
Shady grove, my honey
Shady grove, my true love
Bound for shady grove
[third verse above]
Wish I had a needle and thread
Fine as I could sew
I'd sew that pretty girl to my side
And down the road I'd go
[chorus]
[new verse]
When I was a little boy
My mama told me
If I never kissed a girl
My lips would grow all mouldy
[chorus]
[fifth verse above]
Every night when I go home
(My wife?) I try to please her
The more I try the worse she gets
Damned if I don't leave her
[chorus]
[new verse]
When I was a little boy
I wanted a whittlin' knife
Now I am a great big boy
I want a little wife
[chorus]
[second verse above - with variations]
Wish I had a banjo string
Made of golden twine
Every time I play on it
I wish that girl was mine
[chorus]