The DCs are based upon the standard Diplomacy chart (can be seen at the bottom of the page).
Basically the base DC is 15 to bring one a step up or down.
This Base DC can be modifed by your holding (not sources), and others Law and/or Temple holdings.
In addition of course Regency Points, and any bonuses gained from direct character overseeing.

One can by agitate normally only go one step up or down by each Agitate action.
Exception being by a Crit, which for agitate is gained by first rolling a natural 20, then meeting the DC below
(as an example then, going from Unfriendly to Friendly in one step would be possible by first rolling a natural 20, then meeting the DC of 25)


The Diplomacy Chart:

Initial
Attitude
New Attitude (DC to achieve)
Hostile Unfriendly Indifferent Friendly Helpful Fanatic
Hostile Less than 20 20 25 35 50 150
Unfriendly Less than 5 5 15 25 40 120
Indifferent Less than 1 1 15 30 90
Friendly Less than 1 1 20 60
Helpful Less than 1 1 50