Just noticed this thread isn't actually tagged Pathfinder 1 only (it was started in 2009 so I guess there was no need).
But this does allow me to discuss the thread topic from the perspective of Pathfinder 2!
First off, the price of anything in PF2 is simply set by its level. No, PF2 doesn't provide a direct formula (of the price = LEVEL x 1000 gp kind) but it's still easy to set a price based on a level only. Just check the Treasure Table and you'll see that with few exceptions, every item of a particular level is priced roughly the same.
So if your player is asking if she can purchase a Griffon to have as a mount, you could do much worse than reasoning a Griffon is a level 4 creature, 4th-Level Permanent Items cost roughly between 75 and 100 gold, and put the price on the Griffon on the expensive end of that range: 100 gp or even a little more.
In this I noted that Griffons aren't actually uncommon creatures. I'm aware the fantasy trope says rearing and training Griffons is incredibly hard, but isn't creating a magic sword incredibly hard too?
Anyway, if you do want to treat a trained Griffon as one rarity category higher (i.e. Uncommon) - which for the record is totally reasonable - let's talk about how to interpret the DC adjustments for rarity that are in the game. I'm talking about that Hard +2 is associated with Uncommon, Very Hard +5 is associated with Rare, and Incredibly Hard +10 is associated with Unique. (The most common application would be Recall Knowledge tests for monster information)
Anyway, if we observe that a +2 modifier equates to a 1-2 level increase (the DCs by Level increase by either 1 or 2 points each level), then we can say that an Uncommon Mount (or any other item, for that matter) should cost as if 1 to 2 levels higher.
Now, again per the Treasure table 5th-Level Permanent Items cost between 125 and 160 gp (again ignoring outliers) and 6th-Level Permanent Items cost approx 230 gp or so.
So if you rule that a common Griffon is one that tries to eat you, and that you need an Uncommon Griffon to use as a Mount, you're totally justified to set a price anywhere between 150 to 200 gp I would say. A price hike of at least 50%, which feels reasonable given the nature of the item purchased.
A Rare monster would then cost as an item 4 levels higher (since +5 to DC corresponds to roughly four levels).
An Unique monster would cost as an item 8 levels higher (since +10 to DC corresponds to roughly eight levels).
You might think, shouldn't the GM disallow a player from asking for an Unique mount, or at least consider the willingness of said Unique creature? Absolutely, I'm just pointing out that if you spend all your cash to bring along a L-8 creature on your travels, this will absolutely never be overpowered, since even the least important mook monster will pose a lethal threat to that mount.
It will - by definition! - be at least four levels higher than the mount.
(If at any time you or the other players start feeling uneasy about how the mount provides unbalancing powers, just have this lesser monster shoot it down, and problem solved. Yes, that particular fight became very slightly easier since one of the weakest monsters became preoccupied. But that's an easy price to pay. Of course, if the player is smart and doesn't abuse his mount
(I'm here referring to its movement capabilities in combat), this won't become an issue)
The main takeaway: use level to set prices. It really does work
Z
PS. I'm discussing the pricing of mounts in this thread, not whether the GM allows exceptions from the rather draconic Mount rules of Pathfinder 2. Let me just say that once a hero can afford a Griffon mount she will be of sufficient level where any threat will make mincemeat out of the Griffon*, so I haven't found any clear imbalances. (Yes, a Griffon is a flying mount that's clearly superior to anything allowed by the rulebook, but the player is intensely aware that if she uses it in combat it will likely die, and die quickly, so it hasn't been much of an imbalance since the player dismounts as soon as danger presents itself. Perhaps the clearest indicator of this is that the other players haven't followed suit!)
*) I'm assuming your players are like my players - purchasing a mount is possibly a third priority after a weapon and armor. And after having purchased reasonably level-appropriate weapons and armor, we're easily talking a mount two levels lower than the hero, if not more. You simply can't afford an item of your own level unless that is your highest priority.