Just a simple farming trick I discovered while playing. There might be something much more effective later in the game, but for now this has been quite efficient.
One of the early areas in the game, the Fungal Wastes (located south of the Forgotten Crossroads) has an area near the top left of the map that can be used for geo farming.
Entering from the left, initially two giant mushrooms will spawn in a trap room that you will have to kill before proceeding. After you finish the trap room, you can leave the room to the right and then return. Now only one giant mushroom will spawn along with two small mushrooms. The small mushrooms do not give any geo, but the giant mushroom gives 45 geo each time.
Additionally, the Fragile Greed charm can be purchased from the merchant located in the first right turn coming down from the Forgotten Crossroads. With the Fragile Greed charm you will get.
56 geo each time.
Merchant: He will require 86 geo before he sells you any items.
The Fragile charms he sells are strong, but they will break on death, so it is best to buy with caution.
Bonus: Greenpath Geo Farming
Starting from the Stagway station in Greenpath, exit and make sure your Soul is full. There are several easy enemies just outside to get you there. Exit up and find the two moss knights above the entrance to the boss room. Wake the sleeping knight, then get both knights on the same side of you. Cast vengeful spirit three times. Each knight only takes one attack to kill now. go back to the station to rest at the bench and respawn enemies. Rinse and Repeat!
If you have found the shopkeep in the Fungal Wastes who sells the Fragile Greed charm, I would definitely recommend buying and equiping it. It is very hard to die with this method, the charm increases the geo from the moss knights to 102. The enemies you kill to replenish soul will also drop slightly more.
Gathering Swarm is also helpful in farming. You will collect all the geo from killing small fry for soul without having to take the time to walk over it. This charm is available in Dirtmouth after you have found the shopkeeper in the Forgotten Crossroads.