With Verse there's a conversation option after you find out her relationship with Barik, where you ask her if she thinks that's the cause for her hesitation in the fight that got her sister furies killed.
Eb, I always have at max loyalty, probably it's sort of automatic if you go on the rebel route.
Barik, I don't have loyalty issues with him even while being an enemy of the Disfavored. Following the quest to remove his armor con easily grow his fear.
Sirin lets you gain very major loyalty if you ask her about her mother's death and then follow telling her you won't ever ask again.
Kills in Shadows I believe gets lots of loyalty if you side with the Stonestalkers (rebel route, don't know if it's possible in other routes).
Lantry, never really cared. As soon as I got him I had lots of loyalty.