tl;dr You can use this spell to transform all manner of objects and creatures into new forms—you aren’t limited to transforming a living creature into another living form restates the spell's possible targets not its results; its results are still limited as per greater polymorph plus some objects.
When polymorph any object says it functions like greater polymorph, it means it's precisely like greater polymorph except…
The changes made by the polymorph any object spell to the greater polymorph spell are reflected first in the polymorph any object spell's header entries then in its description.
When the Pathfinder spell polymorph any object in its description says, "This spell functions like greater polymorph, except that it changes one object or creature into another" object or creature, the description echoes the D&D 3.5e spell polymorph any object's description, Pathfinder having changed in that description only greater polymorph from the original's polymorph.
So far, so good, right? And were the polymorph any object spell description in Pathfinder to go from this introductory statement straight into computing the duration of the polymorph any object spell effect—as the spell's description did in Pathfinder's antecedent—, this reader believes there'd be no discussion about how the spell works. However, new to the Pathfinder spell description of polymorph any object is this line "You can use this spell [polymorph any object] to transform all manner of objects and creatures into new forms—you aren't limited to transforming a living creature into another living form." This reader honestly has no idea why this line was added—it brings nothing to the table.
See, one of the traditional restrictions on the spell greater polymorph is that spell's entry of Target living creature touched. So when the description of the spell polymorph any object says, "You can use this spell [polymorph any object] to transform all manner of objects and creatures into new forms—you aren't limited to transforming a living creature into another living form," the polymorph any object spell's description is pointing out that an update has been made to the polymorph any object spell's Target entry.
In short, that line reminds the reader that that the spell polymorph any object has the entry Target one creature, or one nonmagical object of up to 100 cu. ft./level rather than the greater polymorph spell's entry of Target living creature touched. (To be fair, this is an easily overlooked detail.) Thus the new forms in the sentence, "You can use this spell to transform all manner of objects and creatures into new forms," are either new forms that can be assumed via the greater polymorph spell or new object forms, an exception added by the spell description's first line and worded up later in the spell's description.
To be clear, that line in the description of the polymorph any object spell does not change what a target can be transformed into but a reminder of what can be the target of the spell. Just to be extra-clear I'm going to parrot here that line again: "You can use this spell [polymorph any object] to transform all manner of objects and creatures into new forms—you aren't limited to transforming a living creature into another living form" (emphasis mine). And for super clarity: The line does not say, "You can transform objects and creatures into all manner of new forms." (Were the spell to actually instead say that, this reader would totally abandon this position and go with this fine answer!) So the restrictions on the spell's result—those from the greater polymorph spell plus the any object spell's own objects exception—remain firmly in place despite this largely superfluous sentence.
For example, any living creature can be the target of a polymorph any object spell, but so could a creature that possesses the type undead or a Small copper cube, even though such a creature or object couldn't be the subject of a greater polymorph spell. (An undead creature's immunity to effects requiring Fortitude saving throws doesn't extend to effects that also affect objects like the spell polymorph any object.)
Thus new forms that a caster can inflict upon the polymorph any object spell's target remain limited to A) forms that can be assumed with the spell greater polymorph and B) some objects as per the spell's own description.
The remainder of the polymorph any object spell's description actually does bear this out. The spell's description continues, saying, "The duration of the spell depends on how radical a change is made from the original state to its transmuted state. The duration is determined by using the following guidelines," with those guidelines never really contradicting this premise: casting the spell on a Tiny copper cube so as to transform it into a Small fire elemental likely makes the spell's duration only 20 min., and casting the spell on a manticore so as to transform it into a shrew makes the spell's duration anywhere from 1 hour to permanent. (Both durations are ultimately dependent upon the GM's adjudication of the original's and ensuing creature's kingdom and class.)
After the polymorph any object spell effect's duration is computed, the spell's description continues, describing what happens if the target lacks one or more ability scores, explaining that damage in one form (somehow!) carries over if the original form's resumed, how the spell can neither make nor target magic items, how the spell can't transform a target into wealth nor transform a target into some special materials, and ends with—for convenience—what other spells the parent spell can duplicate. None of this contradicts the spell description's first two sentences either.
In sum, the polymorph any object spell just can't transform a creature or object into anything but either an object (and that's limited as per the spell's own description) or a creature that possesses the type animal, humanoid or elemental (as per the polymorph spell) or the type dragon, magical beast, or plant (as per the greater polymorph spell). Transforming the target into anything else remains beyond the spell's still considerable power.
Note: For comparison, keep in mind that the higher-level spell shapechange also limits the forms its caster can assume.
Best Answer
It's weirdly difficult, probably because it isn't something the designers thought anyone would particularly want to do.
Your best bet is probably a carefully worded Wish, and the hope that this being an extremely low-power use of Wish the DM won't twist it on you.
However, there is one explicit way - be a 14th level Wizard of the Transmutation school. Then, spend 8 hours creating a transmuter's stone, and another 10 minutes using the Major Transformation ability. This will allow you to turn one object no larger than a 5-foot cube into another object of similar size and mass and equal or lesser value.
And yes, this is ridiculously restrictive. And it's bizarre that this appears to be the only way, which is why I suspect this isn't something the creators of the game thought anyone would care about.
Even more restricted alternatives include:
For the specific case of making pumpkin carriages, there's a spell that should work for you - Creation. You'll need to cast it out of a fairly high-level slot to create a full-sized carriage, but if True Polymorph is on the menu this shouldn't be a problem. Pumpkin is quite definitely vegetable matter, so it should last a day; plenty of time to get Cinderella to and from the ball. Of course, 100gp would get you a mundane, ordinary carriage, so you could just do that. Alternatively, Wish can create pretty much any nonmagical object, so you could do that too.