Are you using commanders? You can take a commander and level them up twice (or even three times, but it takes a while) on hostile Independent Powers, they don't get the +8 Combat Strength. Your first promotion should be initiative, to be able to drop units from the commander that are active that turn.
There's some argument on this, but as a player that thinks Deity is too easy, I suggest you take manueverability as your second promotion. If you have a unit in the commander, they can cross almost any terrain and get extra movement. There is something the game doesn't tell you here, and that's army commanders have a special civilian slot that doesn't take up any room, so I put a scout in each one so I can deploy all my military units at once while retaining manueverability.
Make sure all your attacks are started from beside the commander to get experience. Take a mix of either 2 ranged and 2 melee units or 3 ranged and 1 melee unit, at least at first. Later it may be more valuable to take 4 cavalry. For getting the initial experience to make your army commander better, it may be useful to take the policy that gives Combat Strength against Independents, or the Militaristic attribute that does the same thing, but better.
Get used to using natural terrain to lessen the damage taken by your units. Rough terrain is best, vegetated terrain is second, rivers are the worst as they actually decrease your unit's CS. This is where you attack from and end your units' turn. If you can, you can build fortifications which are better than either terrain bonus, but they stack with it.
If you took Initiative and Manueverability promotions like I recommend, you can make your next one combat strength for infantry or ranged. From there you continue down the tree to the bottom, without filling out the other side of the tree. When you get to the end you will get a commendation. Take Order, on the far right. It gives +5 CS to any unit starting its attack from the same tile or next to the commander. Now you also have a +8 CS advantage, which can be combined with terrain effects to dominate your enemies.
. Deterrence works well by the way. I always tend to go (my first two civics) for mysticism and then the army commander. If I have the commander, I pack it with at least 3 units (two slings and a warrior) and just move away to destroy every hostile independent for the experience. Build a second commander when you have the earliest option. On deity you will probably be too late for Terracotta Army anyway. Two packed army commanders will definitely deter most AI players up till halfway antiquities. Keep one close to the mos nasty AI. And finally build a third one halfway antiquities. Usually by that time you can put in a siege unit and a cavalry one.
. I do exactly the same. With a bit of luck the first commander can go to level four fighting independents. I try to go for the defensive or the one that gives city bonuses as a third choice for treats. Depending on the game. And the for the order commendation if the fighting continues. But usually I set up three packed army commanders at roughly halfway antiquities. In most games it is enough to deter (most) AI players. And good enough to prevent wars in exploration as well if you focus on relations and trade.
