In my limited experience playing CiV, I have never successfully demanded anything from the AI (no matter how large the disparity in our power), nor have they ever demanded anything from me in a hostile way. Only the all-too-common "requests" from friends. It isn't like Civ III at least, where the AI would demand from you often, sometimes even when they were actually weaker than you.
However, in skummelhustler's and DanielChe6's series of leader dialogue videos on YouTube, where they meet the leaders and then do a number of things like trade with them, make demands of them, and then declare war on them, I have seen a few leaders give in to a demand (and remember, this was the first turn they were met). In those videos, one of the things they say when they give in to a demand is "I will do whatever it takes to keep the peace."
Given that, I wonder what it takes to make the AI agree to demands?