Here is a possible implementation of local currencies. It’s oversimplified, but, I think, playable.
Each sovereign nation has its own currency. (Puppets might or might not use their liege’s—perhaps a decision to introduce their own.) That currency has an value relative to gold (more precisely, the ratio of the price of gold in that currency at the start of the game to the current date, so the Pound Sterling having a value of 1.1 means that £1 is worth 10% more gold now than at the starting date). If the exchange rate is below 1.0, the currency is undervalued, or “weak,” although I think it’s more informative to call it cheap, and if the exchange rate is above 1.0, the currency is overvalued, “strong” or expensive.
All commodity prices are set on the global market, in gold, but paid in local currency. Purchases are converted to local currency by dividing them by the currency value. Sales are converted to local currency by multiplying by the currency value. This means that, when the value of the currency is low, imports are more expensive but exports are less expensive, and when the value of the currency is high, the reverse is true.
Domestic debts, including loans from a country’s own pops to its government, are payable in the local currency, so inflation is good for debtors but bad for domestic lenders. Money borrowed from foreigners is payable in gold. War reparations are paid in gold. Taxes are paid in local currency; reserves are denominated in gold.
The game tracks the balance of payments in foreign transactions, including exports, imports, loans, debt payments, war reparations and remittances from unassimilated immigrants to their families in the Old Country. A country can be on or off the gold standard. If it is on the gold standard, the government makes a percentage of its current-account surplus if it has one (from seigneuriage) but, if it has a current-account deficit, has to spend a certain percentage of it to purchase its currency back and maintain the exchange rate.
If a country is off the gold standard, its value increases if net demand for it is positive and decreases if net demand is negative. The main consequence of this is that your balance of trade usually stays in equilibrium: a trade surplus causes the value of your currency to rise, so your people can afford to import more goods, while a trade deficit increases your exports and decreases your imports. Either way, your trade gets back into balance. If you make a lot of money from selling natural resources, your currency becomes more valuable, so your factories’ costs (such as debts and wages) go up, and therefore your exports are less competitive—which could stunt the rest of your economy.
Every so often, speculators cause a currency crisis, and you’re forced either to spend a lot of gold to defend your currency, or to devalue it. This is more likely to happen if you have a big trade deficit.
Around the time of the Great Depression, you get a choice between austerity and devaluation. If you pick devaluation, you could get hit with hyperinflation if you have a lot of foreign debt, and if you pick austerity, you could get hit with ruinous deflation if your pops are in a lot of debt.