Strategy against 4-legged barbs

[ramses II.]

If I've got writing and I see a couple of 4-legged barbs (horsemen /chariots /elephants and so on), I often disband a warrior (to get some schields in the production box if it's empty) and build a diplo by incremental buying. I often can bribe a barb, capture the barb chief and destroy a 2nd barb. The bribed unit replaces the disbanded unit (->martial law).
In one of my last games there were two "hot spots", where barbs appeared again and again - and I used this trick again and again and made some good cash.
The bribed units were sent to nearby cities and disbanded or rehomed.
Archers and Legions that come from a vessel are fought the following way (if I have city walls and two good defenders in the concerning city). A four-legged unit from a nearby city (or from the attacked city). moves towards the barbs (if the barbs are just inf front of a city, they will attack the city, not the units outside).When the barb archers/legions die, the barb leader moves away form the city - and is caught by my 4-legged unit the next turn. This strategy often works.
Here a little sketch:

---|xxxxx2
sea|
---|B1
---|C

(B=barb C=City 1=4-legged Unit from attacked city
2=4-legged Unit from nearby city
x=some terrain)

[rah]

If there is rough terrain I will move a unit from the city in an attempt to capture the king when the barbs are next to the city.

When there is a spawning area. I just usually leave a defensive unit fortified on a mountain between it and my closest city. Stick a 4 legged unit to round up kings and the barbs will destroy themselves. If this is near an AI city. I'll put a diplo in the stack to bribe non units. You can build quite an army of non-units this way to be used when you change governments.

But playing SP, you don't get time to react to initial landings and spawnings.