At the moment Justicar's Convictions generally go unused for the most part. The main reason why Convictions go unused is the fact that healers can pick up most of healing required. With only the light spot heal required from time to time. Two abilities that might be able to be changed or tweak include:

Doctrine of Valiance is our convention dump skill, but the heal is about the same as the Doctrine of Bliss and the damage is not special. This ability is the idea candidate to be changed.

Doctrine of Righteousness is most likely the least used ability - specifically because it requires the Righteous Manadate to be on the Target first and its the Tanks job to take all the aggro. However it does have some uses for when the Justicar is a off-tank or off-heals.

Current capabilities that Justicars struggle with
Magic damage reduction
Pulls / gathering mobs together

A ability like Precept of Refuge that increased our Magic mitigation by 15-20% - over lap with Precept of Refuge or not and give Tanks a choice when they need to use which ability.

A ability that uses 1 convention to pull on a 30 second cooldown.