The decision algorithm (both in BtS and K-Mod) is to compute for each landmass a total (utility) value of cities. If that total is negative, the AI concludes that keeping the colony is more trouble than its worth and liberates it. In BtS, the per-city value is computed as the city's gold plus research plus production minus three times its colony maintenance.
Strategically, how can you use this information to cause an AI to create a Colony?
1. Make Peace (or actually, a Cease Fire)! From my experience, an AI will not create a Colony when it is involved in a war. Now, I haven't seen the code, but I imagine that it would make sense to program such a special case, to avoid an AI immediately imploding if it got into wars where its valuable Trade Routes disappeared and then started spamming Colonies due to lacking the Commerce for the Cities to remain a net gain in terms of the Colony calculation in the short term. In general, if an AI were to create a Colony, it would make itself more vulnerable, at least in the short term, in terms of warring, so it would seem logical to have a special case that prevents an AI from making any Colonies when involved in any wars.
2. Give the AI more Cities on the same landmass. The more Cities that it has, the higher the Colony Maintenance for each City and thus the higher the total Colony Maintenance across of all of the Cities on that landmass, meaning the more likely it will be for an AI to create a Colony.
3. Blockade! You can't blockade with Non-Privateer boats when not at war, and my belief from #1 is that the AI cannot be at war, so your only option is to use Privateers. But, you can remove the Gold/Flasks components that come from Trade Routes with effective Privateer Blockading, meaning that the Cities will have less value for the AI in the decision of whether the Cities are sufficiently valuable to keep them.
4. Pillage selectively! If you notice, Food does not come into the equation. Trash the Mines, the Cottages, and other squares that have high Hammers and high Commerce, such as Plains Cows Pastures or Grassland Dyes. Leave the High-Food squares, such as a Farmed Corn, intact. The formula is only going to be able to work with squares that the AI's Cities' citizens can work, and if the citizens can be encouraged to work squares with low Hammer input and low Commerce input, i.e. by wanting to work a 5-Food or 6-Food square with a citizen, then the value of such a City will go down in the "keep the Cities or create a Colony" decision. If you aren't at war, sending an army of Spies over to Sabotage improvements can also have a similar effect as Pillaging, especially on an island where an AI might not have an army of Workers to quickly reconnect improvements.
5. If an AI is Financial, is in a Golden Age, or has some other means of improving their Hammers or Commerce (such as having a Unique Building that gives it better Harbours, i.e. Carthage's Cothons giving that City +1 Trade Route), then the AI will value its affected Cities more, meaning that you'll have to work harder to tip the scales in your favour, such as by gifting the AI even more Cities on the same landmass.
6. How can you see Colony Maintenance values? Use a test game that has similar settings, World Build the AI's Cities, and gift yourself a Great Spy in one of the AI's Cities to Infiltrate, and you should have a pretty good estimate. Note that Colony Maintenance will increase as the size of the Cities increases, so make sure that you're assigning the same City Size values as in the real game to get the most accurate picture possible. Alternatively, if you have Espionage Points to burn, go ahead and use the Espionage Screen (Ctrl + e) to focus them on that AI and earn the ability to double-click on that AI's Cities in the real game to see the City View of each relevant City.
7. If the AI's Cities are well-developed in the later game, use Spies to destroy Courthouses or similar Colony-Maintenance-reducing Buildings, such as the Zulus' Ikhandas.
