There was a recent query on EE for a novel titled The Songs the Trees Sing or some such. I had a nice time spending 15 minutes coming up with these bits in a comment (which I'm sure was very helpful to the author):
The songs the trees sing: Woody Guthrie.
What did the lonesome tree sing to his sweetheart in another forest? I pine for you.
What did his friends call the tree who sang love songs all the time? Sappy.
What did the kind critic say about the tree actor? His performance was wooden.
Why couldn't the tree family get any sleep? Their pet tree barked all night.
What's a tree's favorite Sesame Street character? Grover.
Favorite deodorizer? Glade.
Favorite female name? Maple.
Favorite male name? Ash.
What nickname makes all the school trees snicker? Woodie.
What did the blogger trees say to each other when they saw paca's puns on EE? Let's leave.
I should have added this one, too, though it isn't a pun:
What material did the spiteful tree use to build his furniture? People.