Philosopher's Stone has an inherent problem: It needs a lot of cards in your deck (that you can't play), but this means you'll see your Stones less often. It's a paradoxical card. You can't really rely on it being your main source of income, so you can't really create a deck for it.
Philosopher's Stone is typically something you stumble into buying because you already have a Potion for another card you wanted. It makes for some tactical decisions: Do you buy one more Familiar to win the curse war or get a PS instead, getting a better long term reward?
PS could be much more interesting if it didn't require a Potion, it would have made a decent promo actually, because of the card counting thing. It's just a shame that very few cards can do anything useful with it due to its paradoxical nature. What can deal with a bloated deck in which you need to find particular Treasures? I can only think of Adventurer of the top of my head and Herbalist has its novelty topdecking thing going on.
Pstone's big problem is that it is pretty much solely a source of +coin and all sources of +coin have to compete with Gold and Silver. Unlike with say trashing, there are very few times where what Pstone gives is
only possible with Pstone so it has to clear a much higher opportunity cost to be useful.
For instance, Scavenger can fairly reliably cycle Pstone. Open Scav/silver -> buy a pot -> Scav the pot (buy a Pstone) -> (buy Scavs) -> Scav a Pstone. It doesn't take long to get to 25% of your deck being Scavs and hitting Pstone/Scav every turn. The problem is that you need 15 cards in the discard/draw deck to be competitive with a simple gold. With 5 in hand, that is 10 turns into the game to equal gold and 15 to beat it. With gold/silver as benchmarks you need a very quick ramp up to make Scav/Pstone beat Scav/BM.
What can provide that? You can have a sunk potion cost from Familiar. You can have cheap +buy (say from Candlestick maker) to bulk out the deck. You can have something really nice like Traveling fair (extra +buy, no action cost). Junking attacks (add free bulk, make game longer) can make the difference between $3P and $6 a lot more significant. Colonies can let you go longer and have efficient VP for when the Pstone gets strong enough to matter. Black market can lower the opportunity cost (you can play the Pstone and then continue drawing; this might even make Pstone not totally crappy with Storyteller, but I doubt it). But all this stuff is insufficient on its own, most often you are looking at 3 or 4 card combos here.
As of yet, no card causes Pstone to be drawn more often than gold, and even most of the ways to draw either over other cards just aren't that great (Golem skips both, Venture/Adventurer has to deplete coppers, Sage gets stuck on Pots and Green, and Hunting party/Journeyman end up being not so hot in practice). It rarely benefits from trashing or drawing (as needs a lot of cards to beat Gold); and even sifting does relatively little (8 cards cycled via Storeroom is around the max and that isn't enough to make Pstone beat Silver and hit every turn without a lot of build time).
So we have a card that costs
almost as much as gold (and absolutely more than silver), takes a lot to make worth more than gold, and cannot be drawn more frequently than gold (barring edge cases it is almost universally going to be drawable less often than gold). Why would we ever buy it over gold unless we are already sitting on a Pot for some reason (or on a functional equivalent like Loan/Mine)? Even when we have the pot, how often will it really be competitive with Gold when Gold works so much better with every engine enabler (+cards, trashing, etc.)?
Only a few rare tactical plays come to mind:
1. It stores potion value for later. Want an Apothecary/Golem next turn when you have a Develop? Okay that happens every so often (particularly if you play Base/Alchemy/one other expansion). Mint is a fun mention here as it is one of the few ways to gain Potion value without using a +buy (Mint a Pstone, Remodel it into a Golem, buy something else with your lone buy). Another is Stonemason as already noted. It can also be worth it to pull useful value out of Familiars after curses run out (e.g. Butcher a Familiar to a funny Silver/Gold) or to get Graverob value out of a Transmute (say after you're done killing curses in a University deck with Unis gone from the supply).
2. Fun with top decking late game. It can be worth it to dump a Pstone on deck top with Watchtower, particularly if you can pair it with something synergistic like Storeroom; 6P just might be left over change in an engine when there are no more Universities and with just 27 cards that assures a province next turn. Herald is another option, though you often need to sacrifice a duchy or province to set things up (though with something like Counterfeit it could work once in a long while).
3. Use it as a not-totally-useless-unique card. It does play well with Horn (2 unique cards that don't need +action) in marginal Horn decks and can juice Forager for similar reasons.
4. Juicing mass discard setups. Something like Inn/Cellar/Council Room really can draw the deck and leave a good bit of fodder for Pstone to build value. Other options include things like juicing a mass Madman/Storeroom setup (where each Pstone could be a province in a megaturn) or big Nv discard setup (e.g. Gold/Pot/Nv/Nv/Courtyard/Iw where you can gain a +buy and have an unlimited discarder on the mat).
5. It resists mass Noble Brigand. I've seen once where it paid to go Pstone against Kc/Nbrig. No other +coin (+value), only draw was Pearl diver or something, and heavy trashing. So you either needed Kc/Kc/Nbrig/Nbrig/Gold, or you needed a deck that could stand mass copper & mass treasure stealing.
6. It defends against Smugglers, Knights, and Giant.
7. It is less likely to be Embargoed than Gold.
Pstone's ultimate problem is Gold. Gold does most everything Pstone wants to do, better. It is just marginally harder to buy Gold early game and possibly less valuable late game; otherwise pretty much every comparison favors Gold the vast majority of the time.