I found quite a few farming methods, online. The two best methods appear to use a combination of augments to farm other resources and convert them directly into koin. This is especially useful, as you can remove augments along the conversion path to farm the other resources, as well.
Farming with Frost
I found this video on YouTube that details a specific build for farming koins with Frost. Using the "Cold Efficiency" and "Snow Piercer" augments for easy flawless victories, and the "Perfect Kombat" augment to reward additional hearts for flawless victories, you can then use the "Heart and Soul" and "Dark Magic" augments to convert the hearts into koin. The build shown reports that it can earn 2,500,000 koin per second. It might be a grind to unlock the required augments, but it would definitely make grinding all the required koin considerably easier.
Farming with Krushing Blows
I found this video on YouTube that details creating a build to farm souls by using the "Pure and Simple" augment to remove the requirements for krushing blows and the "Smoke and Mirrors" augment to remove the limits and damage inflicted by krushing blows. You then use the "Spirit Collector" to earn spirits with each krushing blow. With this build, you can set up a match and spam krushing blows to farm souls. By adding the "Dark Magic" augment, you can convert the farmed souls straight into koin.
Sending AI-Controlled Characters into the Endless Tower
I found this video on YouTube, where you send an AI controlled fighter into the endless classic tower. You have to be present to press the confirmation button, between rounds, but you are free to do other things while the AI fighter earns you koin. AI fighters appear to prefer using fatalities and brutalities, so this also earns you hearts.
Farming the Krypt
I found this video on YouTube, where you unlock soul fragments by completing character towers, and then go to the Krypt and open as many soul fragment chests as you can. Spend koin to replenish the soul fragment chests, then wash and repeat. You earn more koin than you spend, as well as soul fragments.