The owl and the pussycat
The nursery rhyme with the initials TOATPC is "The Old Woman and the Pig," which is a traditional English folk song about a woman who asks for help to retrieve her pig from the garden.
Bagcotp
The nursery rhyme with the initials MPHAD is "Mary Had a Little Lamb."
The nursery rhyme with the initials "BSWTS" is "Baa, Baa, Black Sheep."
The nursery rhyme with the initials IRIP is "It's Raining, It's Pouring."
The nursery rhyme with the initials "TITWTLR" is "Twinkle, Twinkle Little Star."
The nursery rhyme with those initials is "A Pocket Full of Rye."
The nursery rhyme with the initials TMTM is "Twinkle, Twinkle, Little Star."
The nursery rhyme with the initials IYHAYKICYH is "If You're Happy and You Know It, Clap Your Hands".
The nursery rhyme with initials FLSF is "Five Little Speckled Frogs." It is a popular counting rhyme where each verse features a frog jumping into the pond.
The nursery rhyme with the initials SLMSDTS is "Mary Had a Little Lamb."
The nursery rhyme with the initials LLFAH is "Little Miss Muffet." It tells the story of a young girl who sits on a tuffet, eating her curds and whey, and is frightened by a spider.
a nursery rhyme
Probably one that starts with "one, two, three, four, five".