More that 2 units per city in NOT necessary if you know how to position your troops. This comes from my experience, so it's not an exact science. But after a lot of Emperor/DG level games where I play through the middle ages averaging between 1 to 1.5 units per city, I think the following rules are correct more often than not:
How to Position Troops to Prevent AI Attacks
1) strategic resource cities -- The AI loves to attack cities that have strategic resources within their radius. Never leave such a city undefended. Always defend these cities more heavily than other cities. If your military is so thin that some other cities are left undefended, then these cities should have at least 2 units in them. Otherwise they need 3 units.
2) Border cities with culture conflicts (and especially if you're winning the culture war!) -- A city has a chance to culture flip if any of its native 21 tiles are in another nation's control. The AI don't like that. The fact that it may lose a city culturally is a major incentive for it to attack. The likely hood of this kind of attack, in my experice, is right behind lightly defended resource cities. This type of situation also deserves 2-3 defenders.
3) Any cities or large worker stacks on the border -- If it's something that the AI can reach
this turn, then it should have some kind of military cover. 1 unit is enough.
4) The same rule applies for AI units traveling through your territory. Have your units shadow their movement, and fortify in cities along the way. This is where tight city spacing, having mobile unit, and NOT signing RoP really helps. Your response to AI troop movement should be proportional to the AI troops numbers. For large AI stacks, 1 unit per city is not enough, which is why sometimes it's more troop efficient to just block off your heartland with units, which will stop this kind of friendly, but dangerous AI movement.
5) Provision for the more aggrssive AI's -- The Zulus, Germans, and Mongols are the most aggressive AI's in the game. The Persians, Romans, Vikings and some other AIs can also be pretty aggressive. Any AI that has no room to expand may become aggressive. Put more troops on a border shared with these AI's. To put it in another way, if you're stuck between the Zulus and a hard place -- build troops
6) And, rest of the cities can be left undefended! This is where the saving in troops comes in.
Summerizing all of the above, the amount of units needed to be "safe" is a function of the lay of the land, the composition of the neighborhood and your decisions of where to found your cities. These factors change from game to game, and so should the amount of units you build!
In a game where you have a very short land border, no culture conflict, and very little native resouce, averaging 1 unit per city can be "safe enough". On the other hand, if you found a city that takes away Iron from the Romans, then you need to pile units onto that spot.
I learned personal diplomacy decades ago, but used to get beat up as a kid. I fight now in the game when it seems necessary, and it's getting easier, but I'll probably never become a real warmonger. 
