Yes, pony's is the correct singular possessive form.
example: The pony's stall was very clean.
The correct spelling of the possessive form of "people" is "people's."
The correct spelling of the possessive form of "women" is "women's."
The correct spelling for the possessive form of "college" is "college's."
monies'
kids'
heroes
The singular possessive form is story's.
The possessive of scientist is scientist's (apostrophe S).
The correct possessive form of dynasty is "dynasty's."
companies'
contractor's
falcon's