Как отмечено в предисловии, песня происxодит из отсталых южных штатов США и потому небезупречна с точки зрения грамматики.
Hush little baby, don't say a word, Mummy's gonna buy you a mockingbird. (= Mummy is going to buy you... = мама идёт (собирается) купить тебе...)
And if that mockingbird won't sing, (won't = will not, после if правильнее было бы doesn't) Mummy's gonna buy you a diamond ring.
And if that diamond ring turns to brass, Mummy's gonna buy you a looking glass.
And if that looking glass gets broken, Mummy's gonna buy you a billy goat.
And if that billy goat won't pull, Mummy's gonna buy you a cart and bull. (правильнее: a cart and a bull; впрочем, пропуск оправдан тем, что здесь cart-and-bull как бы склеились в одно слово).
And if that cart and bull turn over, Mummy's gonna buy you a dog named Rover.
And if that dog named Rover won't bark, Mummy's gonna buy you a horse and cart.
And if that horse and cart fall down, You'll still be the sweetest little baby in town!