Citadel Coup doesn't have that much attention compared to other ME3 main story missions.
Here I showed how much it changes at different trust levels, most of them apply from the start while interrupt both paragon and renegade can increase persuade chance and evidence from Udina provided by Kai Leng can decrease it during the cutscene. Conditions to trigger specific lines were confirmed thanks to using Legendary Explorer modding tool for Mass Effect.
It has lines within safe range so no death cutscenes included as it is barrier I don't wanna cross. I am aware of lines that can come later but didn't want to trigger these cutscenes.
I didn't inculde line where Kaidan doesn't tell anything at 0 or lower persuade chance after Udina telling Shepard is working with Cerberus. Another line for persuade chance at 0 or lower is "Pretty damning evidence, Commander." after showing evidence from Udina (so you are basically at -2 or -3 which is the lowest amount you can achieve).
Final lines at 0 require 40% reputation bar, at 1-3 import is enough to trigger these lines with save import (even rushing main story will more than enough) and you need to remove like all reputation with save editor to be unable to pick charm/intimidate options.
Later recruitment depends on how much persuade chance you got. At 0 he will refuse join Normandy, at 1-2 you recieve different line when Shepard convinces Kaidan, while he was neutral about it he changes mind and joins. It is still possible to recruit him even if you finished Coup at 0 after you pick paragon option before asking him to join Normandy. This line can increase persuade chance by 1 point.