Hey, Blue Tempest:
This sounds like a fun plot point! What exactly are the PCs relation to the counterfeit coins? Are they trying to figure out who is doing it so they can stop them?
Since it's for storytelling purposes, I would just make the counterfeits look like real gold coins and just require a perception check (DC 20 or so?) to notice any irregularities and an appraise check (DC 20 or so?) to affirm that, in fact, it is a counterfeit gold coin.
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I don't think you'd need to mess with anything too complicated to get that plot point to work.
Plus, what are you valuing the coins off of?
I bring this up since coins of premodern era were valued off of the value of the rare metals in them- thus, they are 'gold', 'silver', and 'copper'. It is a fairly modern thing for the value of currency to be divorced from the value of the materials used in making it (typically based off of a government promise that 'this bill is worth X amount of gold').
So I would suppose, withthe mention of weight, you would want to attempt to basically gold plate some cheaper metals. In which case, I would rule that you would need some type of check to make them authentic. Most likely a craft check (in which case I would use crafting rules- 1/3 the price of the finished product; also have the check work for opposing an appraise)
Of course, with wizards with crafting spells that could do such a trick in mere minutes with the raw materials... I would imagine that there would be many that create magical tools to deal with this problem (I particularly imagine that the church of abadar would subsidize such projects- he is a god of cities and trade, after all, and counterfeiting ruins the trust in both). Hell, I would imagine official currency might even have magical watermarks designed just to make it harder to counterfeit an item that is typically considered mundane.
I realize all that, so I'm trying to think of a work around or something more obscure that maybe even governments haven't figured out around yet. Like maybe a certain magic spell that's not easily removed or noticeable.
Well, the problem here is that we are discussing the economy in a game derived from D&D. So actual realistic considerations are thrown out the window from the game design, and it all comes down to reasonable GM fiat based off of his authority to handle the setting.
IE- you may not even face any detection methods at all, since your GM didn't think of any before you started counterfieting, and the later retcons some in that work on the same principle of 'rocks fall, everyone dies'. So whatever you come up with, you will likely find a higher ranked official that say "oh, that silly trick. Yeah, this doodad beeps whenever somone tries that".
The best answer I can give you is 'magic aura', which can help fake aura on items. The key problem with that is that it is one item per spell, which means way too many to be practical.
The key problem here is that it will be extremely hard to find any effective countermeasures that don't bash up against the fact that coins are meant to be held in the dozens or more.
Honestly, it is more cost effective to counterfeit expensive items worth hundreds of gold (+1 swords under the effect of magic aura, for example), and then disappear before anyone notices. Then, the gold you have would be real, and you probably needed less checks for the same general actions.
It's not something i'd ever considered, but does currency in pathfinder have any magical properties by default?
I just assumed they were lumps of gold, pressed with a design.
In which case a counterfeit coin would be a lump of "not-gold" pressed with a design. So there'd be these ways of spotting it:
appraise(?) to determine material isnt gold
appraise(?) or craft(?) to determine the design is wrong.
If coins arent normally magic then a detect magic or similiar would show there's something up with the coins. at which point dispell or something would come in handy.
Regardless, i doubt many people would think to check anything beyond the material of the coin, there's usually a surprisingly high rotation of fake currency in any country's economy after all.
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Your basic Prestidigitation cantrip can colour items for an hour: so for a short term counterfeit you could stamp yourself out some coins with the design of gold coins, but of some other material of a similar mass, and use the cantrip to colour them 'gold'. Prestidigitation doesn't effect feel or taste or hardness though, so any merchant worth the name will probably spot such fakes quite quickly with ye olde fashioned 'bite the coin to test it' method. Still, a chest full of counterfeits with a layer of real gold coins on the top could possibly work... maybe with some sort of Bluff or Sleight of Hand check to direct anyone sampling the coins to sample the real ones, rather than the fakes?
I'd suggest a custom spell based off Lighten Object to make coins of some cheap alloy feel as dense as gold. The softness and feel shouldn't be a big issue, medieval/renaissance coin gold wasn't that pure (if not quite as bad as Terry Pratchett's 'approximately the same gold content as seawater') and wouldn't be as soft as modern gold.
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Older editions had a spell called fool's gold, second level wizard I believe, that made objects look and feel like they were made of gold. IIRC, tapping such an object with an iron bar dispelled the illusion. So you could go that route and make a custom spell.
If you want to go mundane, I'd suggest Craft. Several Craft subskills could justify making fake coins - alchemy, sculpture, jeweler. Generally the idea is to put a thin layer of gold or pyrite over lead. That way the coin looks and feels genuine.
Another trick, which is less about counterfeit and more about taking advantage of poor minting processes, is to shave coins. Basically old coins were not as consistent as the ones we are used to, so you could subtly hack off pieces of metal and pass it off as "wear." Then you could collect your bits of gold or silver and sell them by weight to make extra money.