One day a friend was killing Nathyn's guards for exp. I went and joined him, so I took some Nathyn
faction hit. I probably helped on a dozen guards.
A few months later I started looking at the loyalist shield quest. This quest needs good Nathyn faction.
So I have been killing Coterie every chance I get to fix faction. I've probably helped slay 100 of these and I am still threatening with Nathyn's guards.