There's nothing to stack
An unchained barbarian does not see her Constitution score increase when she rages. That is, the unchained barbarian's rage says
While in a rage, a[n unchained] barbarian gains a +2 bonus on melee attack rolls, melee damage rolls, thrown weapon damage rolls, and Will saving throws. In addition, she takes a –2 penalty to Armor Class. She also gains 2 temporary hit points per Hit Die. These temporary hit points are lost first when a character takes damage, disappear when the rage ends, and are not replenished if the barbarian enters a rage again within 1 minute of her previous rage.
These temporary hp an unchained barbarian gains while raging are, essentially, an easier to track replacement for the morale bonus to Constitution received by a traditional raging barbarian, much like the bonus on attack rolls and damage rolls are an easier to track replacement for the traditional raging barbarian's morale bonus to her Strength score.
Were an unchained barbarian to benefit from an effect that increased her Constitution score, she would while raging gain the temporary hp from the rage and additional hp from her increased Constitution, but a typical unchained barbarian gains no bonus to her Constitution score due to her rage.