Here's how it appears in the sheet music (See Al Maloney's link above. And thanks, Al, for letting me know about a source of sheet music I've never run across before!) Note there is an extra verse not in the version sung by Ada Jones; and it doesn't have the "frog/croak" pun.

THEY ALWAYS PICK ON ME
Words, Stanley Murphy. Music, Harry Von Tilzer.
New York: Harry Von Tilzer Music Pub. Co., 1911.

1. When I was born, my pa and ma,
They looked at me and said, "Oh, pshaw!"
The doctor said, "It's a girl, I think,"
And Pa went out and got a drink.
Then Ma said I looked just like Pa,
And Pa said I took after Ma.
Aunt Jane said I looked like a quince,
And I've been a stepchild ever since.

CHORUS: They always, always pick on me.
They never, never let me be.
I'm so very lonesome, awfully sad.
It's a long time since I've been glad;
But I know what I'll do by and by:
I'll eat some worms and then I'll die,
And when I'm gone, you wait and see,
They'll all be sorry that they picked on me.

2. My ma put me to bed and said
The angels watched me in the bed.
They wouldn't let things frighten me.
Then the angels started biting me.
When my ma sends me to the store,
I lose the change, then she gets sore.
I lost my cat and my bow-wow.
I think I'm losing something now.

3. One morning just at four o'clock,
Somebody tried to pick our lock.
I knew 'twas Papa sure as sin,
And opened the door and let him in.
My ma said, "What time is it, Pa?"
"It's twelve o'clock," my pa told Ma.
Just then, the cuckoo cuckooed four,
And Pa made me cuckoo eight times more.