The Nursery Rhymes were part of the Doll Room Challenge Tim and Matt undertook in season 1 in the seventh episode entitled Mermaid Tails in order to get the antidote for the poison. Matt took a second dose of poison and died in this challenge.

Many, if not all, of these rhymes are about violence and/or murder.

Nursery Rhymes

Timothy's Nursery Rhymes

1. Lizzie Borden

Lizzie Borden took an axe 

and gave her mother 40 whacks.

When she saw what she had done

gave her father 41.

2. Old Father Longlegs

Old father Long-Legs
Can’t say his prayers:
Take him by the left leg,
And throw him down the stairs.

And when he’s at the bottom,
Before he long has lain,
Take him by the right leg,
And throw him up again.

3. Black and Blue

I charge my daughters every one

To keep good house while I am gone,

You and you and especially you,

Or else I'll beat you black and blue.

Matt's Nursery Rhymes

1. Little General Monk

Little General Monk
Sat upon a trunk
Eating a crust of bread;
There fell a hot coal
And burnt into his clothes a hole,
Now little General Monk is dead.
Keep always from the fire,
If it catch your attire
You too, like General Monk, will be dead.

2. Dead Was She On Friday

I married a wife on Sunday,
She began to scold on Monday,
Bad was she on Tuesday,
Middling was she on Wednesday,
Worse she was on Thursday,
Dead was she on Friday,
Glad was I on Saturday night,
To bury my wife on Sunday.

The third nursery rhyme isn't specifically mentioned, but it is speculated it is this.

3. There Was an Old Woman Who Lived in a Shoe

There was an old woman who lived in a shoe.
She had so many children, she didn't know what to do;
She gave them some broth without any bread;
Then whipped them all soundly and put them to bed.