Well, I surprised myself. It was either that I focused my entire horde on them, everthing but I think 5 garrison Keshiks, or that they were underpowered. I think it was the former, because IRL the Mongols fought the Khara Khitai at the same time or earlier.
Overveiw of the Chin
It was in this campaign that I noticed a few things: the complete lack of dedicated infantry for the Mongols, the fact that all cities are size one(!), the excellence of a hit-and run strategy, and the greatness of armies of armies.
As in RL, the Keshiks work best if you use hit and run tactics. If you are playing against the Chin, for example, kill one of their longbowmen, retreat, and wait for the rest to come after you. I never lost a single Keshik defensively, and only I think two offensively, which is realistic, because of the Mongol strategy of retreat. A false withdrawl also works in Civ3, as it should... I just noticed this now because you need four movement to do it properly.
The China are easy enough, all you really have to do is outflank them. If you focus your attacks on the northern frontier, then switch to attacking the southern frontier, they will send their longbows back and forth and in effect, do nothing.
Also, did I mention an army with a 7 attack unit ROCKS!?
Anyway, now the sugestions:
1. The chin are underpowered, however, I think that this will need probably no solving. Al you really need to do is give them bigger cities, which I assume will come later.
2. Combat is coming along really well. The Mongol signature tactics actually work! (A rarity in Civ 3 at best)
3. The Mongols are very stretched by this time; they have to use fifteen or so Keshiks to hold the China and Hsia down. This is realistic, actually, since they actually were quite stretched, but I would give the Mongols the tech fuedalism, and with that include a unit: "Mongol Foot Archer" Stats: 3/3/1 cost: 20 sheilds, maybe, given that they are going to have a hard time building anything with the resisting Chin cities. It should require nothing, but you should give them maybe two in the beginning, garrisoning their two home cities so we can use all the Keshiks to attack and rampage.
All in all, it is coming along quite nicely. Good job on the scenario!
Oh, and just for fun, screenshot of the conquest of Chin (next I think is Khara Khitai, their horsemen riding around my empire are quite irritating):