1. It doesn't matter how many cities the AI have, just camp 1 quechua right next to each of their cities. This would prevent their workers from improving the land and hooking up resources. They usually will stuck with 2 cities producing archers like forever which give us plenty of time to do whatever we please.
2. You will notice that the AI will keep exactly 2 archers defending each of their cities. Every now and then, they will finish producing the third archer. Guess what they will do with the third archer? They send the third archer on a suicide mission with less than 10% chance of success against your fortified quechua. If you camp your quechua in the forest/jungle/hill, it doesn't talke long for your quechua to get 3 or 4 promotions by just standing there. Btw, even if your quechua is at half strength, don't worry, stand the ground because the other 2 archers would not dare to attack. By the time he heals up, another third archer will come out to die.
3. Once in a blue moon the AI may get lucky; so you may want to send out an extra quechua or two just in case. If you have a worker, you can use him to lure one of the archer out then you would have only 1 archer to deal with. You may already hear people saying that the worker baiting trick doesn't always work, but it does work 99.99% for me.
Note: The secret is to camp just 1 quechua, not 2 or 3. If you camp more than one, the AI may abandon their suicide mission. Once they have changed their minds, it will be tough to convince them otherwise. They might be a suicide fanatic, but they aren't stupid. If you have more than 1 quechua, don't stack them.