Am I missing something?

[Egg Bub]

Playing as GB, 1865, my private capital stabilizes at around 20000 and my state funds are at 42000 and increasing. My taxes are very low and I fund most research (apart from stuff like "anarchism"!). How can I burn more cash?

[loki100]

colonialism is a good cash burner, the provincial decisions - telegraphs/sewers/universities all help

but with the gold and gem mines you have I guess at this stage you are going to be very cash rich.

[Egg Bub]

I suppose too much money is not exactly a problem, but if it goes on too long it will get ridiculous. Maybe I should set taxes to 0% for a while.

[Jim-NC]

Are you purchasing things from other countries? If so, pay extra for everything. You can also shut down most of your factories, and purchase stuff from abroad (it is usually more expensive then making things yourself).

Building a large army drains state funds.

[Ebbingford]

Use taxes to build up the army and the navy......

The Naval Defence Act 1889 was an Act of the Parliament of the United Kingdom, instituted on May 31, 1889 to adopt formally the country's "two-power standard" and increase the United Kingdom's naval strength. The standard called for the Royal Navy to maintain a number of battleships at least equal to the combined strength of the next two largest navies in the world

[Kensai]

For a further challenge you can write a small script that saps this extra state funds and private capital and partition it to smaller allied nations that are in trouble. You could even think to author an event (in your alternate timeline) to justify such action.

[Random]

Use taxes to build up the army and the navy......

Far more than just about battleships and the Two-Power Standard, the Naval Defence Act also included a huge cruiser building program to protect the sea lanes and massive naval infrastructure improvement throughout the Empire to base them safely. In PON these can be translated into upgrades of harbours, coaling stations and coastal fortifications with their associated garrisons and guns and are handy ways to burn off excess government funds.