My version starts in the usual way, except change Mama below into Papa.

Hush, little baby, don't say a word,
Mama's gonna buy you a mockingbird.
And if that mockingbird don't sing,
Mama's gonna buy you a diamond ring.
And if that diamond ring turns brass,
Mama's gonna buy you a looking glass.
And if that looking glass gets broke,
Mama's gonna buy you a billy goat,

THEN

If that billy goat gets boney,
Papa's gonna buy you a cart and pony.
If that pony runs away,
Papa's gonna buy you another some day.
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I think I learned this in grade school in the 1950's. I like it because bringing Papa in gives the baby a whole family, and the promise that Papa can buy another pony gives the baby security.