Crown Trick

This will come naturally as you play but what makes this go much faster is saving Stein from City of Steam and upgrading a few passives that increase gold drops. Secondly, completing the boss at the end of the first area will give you a good amount of gold. And finally, once you reach Ocean Depths for the first time the game will start throwing Challenge rooms at you that require you to defeat enemies while meeting certain conditions. If you meet the conditions and get 3 crowns (equivalent to 3 star rating) you'll get a chest full of gold (approx 500 Gold) and with your passives that could very well reach 650-700.

As you can see here, I completed a challenge room that required me to use my melee attacks as little as possible. I simply killed the 2 enemies in the room with my Familiar and got 3 crown rating which gave me an Ultimate Chest that contained approximately 600 coins.

There are also shrines that will double the amount of coins you have on you, an endless challenge that rewards gold for every wave of enemies you survive and many more ways to earn lots of gold.