Here is how the AI "teams up" against you.
Shortly after you start the game, you'll receiving messages saying something like "Tiglath-Pileser changed to Enemy". All the civs that say they became an enemy are implacably hostile to you, and are teamed up together against you. The civs that did NOT say they became your enemy are neutral towards you.
When you play vs. 2 CPs, both are hostile. When you play vs. 3, 2 are hostile. When you play vs. 4 or 5, 3 of them are hostile. When you play vs. 6 or 7 CPs, 4 of them are hostile.
Now, the "neutral" CPs will turn hostile if you attack any of their units twice. This includes towers shooting their explorers or scout boats shooting their fishing boats. That "attack twice" happens pretty fast, so if you don't want to make them hostile right away, you'll need to change your own diplomatic view towards them to Allied (that's the only way to be sure you won't inadvertantly attack them).
In addition, the neutral CPs will turn hostile anyway 10-15 minutes into the game if you don't tribute 1000 resources to them by that time. If you _do_ make the tribute, they become your ally. This alliance is permanent until you (duh) attack them twice. Which if you're allied will only happen if they get caught by the splash effect of an elephant or a catapult stone. Good luck.