Good items for Minecraft currency?

Solution 1:

Diamonds could be used as a currency as they cannot be easily farmed, unlike emeralds. They are rare enough to hold value and were a popular option on servers I have played on in the past (ones that did not use an economy mod).

Alternatively, as x-ray texture packs can be a problem, you could use raw ores as a currency. Iron ore blocks would have the lowest value as these can be obtained the easiest. Likewise with gold, albeit somewhat rarer, and as such would have a higher value. Diamond would be the second rarest as you would need Silk Touch for this. Emerald ore would be the rarest as these are rare to find and have very small veins. You could then assign a value to Coal, Lapis and Redstone ores.

With Iron ore as the base currency, the following values could be used for the other blocks, as the number of ore blocks to iron ore.

Gold ore: 1/2 (1 gold ore for 2 iron ore)

Redstone ore: 1/3 (1 Redstone ore for 3 iron ore)

Lapis Lazuli ore: 1/4 (1 Redstone ore for 4 iron ore)

Diamond ore: 1/8 (1 Diamond ore for 8 iron ore)

Emerald ore: 1/16 (1 Emerald ore for 16 iron ore)

Solution 2:

Looking through https://minecraft.fandom.com/wiki/Non-renewable_resource and using your restriction of non-craftable, finite, and not found in random structures, I'm not sure anything actually meets those criteria. But if you're looking for something with a set number in a bounded world, cobwebs stick out in my mind as something not mentioned so far.

They can be used decoratively use purposefully, which makes them something to worry about using as payment or not. They're not too easily harvestable, as you need to purposefully go looking for mineshafts or the rarer zombie village with shears on you.

They're probably a little more common than diamonds as a 'currency', but once they're all mined there's no other way of getting them, like diamonds.