this is what they have in the faq
How many units do I need to suppress a culture flip?
the full formula (this is from Sorenson, who is responsible for this programming):
P=[(F+T)*Cc*H*(Cte/Cty) - G]/D
where:
P = probability that it will flip this turn
F = # foreigners, with resistors counting double
T = # working tiles under foreign control (out of the max of 21, no matter what the cultural boundaries are atm)
Cc = 2 if foreign civ has more local culture than you, 1 otherwise
H = .5 for WLTKD, 2 for disorder, 1 otherwise
Cte = Total culture of the foreign civ
Cty = Total culture of your civ
G = # garrison units
D = factor based on relative distance to capitals
Now reorganizing this gives the required garrison as:
G = (F+T)*Cc*H*(Cte/Cty)
As you can see there is a nice set of extra factors there. Now when you take a city Cc is likely to be 2 for a long while. And then there is the culture ratio. And this is a true ratio so it could be 1.1:1, 2:1, 5:1 depending on how much culture each of you has
The national culture factor is probably the reason why some seem to have no problem with culture flips and others do. Since if you have strong national culture, this value might be approaching 1/2, which can keep the garrison down at a 1:1 ratio. However, if conversely the AI civ in question has double your culture, you are going to need 4 units for every foreigner and tile to prevent a flip.
Thank you, etj4Eagle !!!