Given that an existing stunt gives a +2 bonus to all emotional defense rolls, another stunt that gives +2 should have a similar limitation like "all mental defense rolls" or "all spiritual defense rolls". ("mental" stress actually applies to emotiona, mental and spiritual damage, not just mental)
Are you talking about Calm Blue Ocean? I'm not convinced that "Gain +2 to Discipline when rolling to keep emotions under control" is the same as "+2 bonus to all emotional defense rolls". For example, Intimidation, a skill used "for producing a sudden, strong, negative emotion in a target—usually fear" can be defended against by Discipline, Presence, or Rapport.
Even so, a character with a Demonic Co-Pilot could easily find themselves asked to make dozens of these rolls over the course of a scene, especially if they have a skill/stunt combo that guarantees success on nearly every roll, as this one could. Barring the occasional fight against WCVs (your mileage may vary in campaigns revolving around heavy WCV activity) I suspect that emotional rolls tend to be much more situational. A roll to determine if your courage fails when pressed by a monstrous presence attacking from the dark. A roll to determine whether you lose your cool in the face of taunting. And so on. Generally these things don't happen several times per exchange, which is possible for the Demonic Co-Pilot issue.
As an aside, the fact that Demonic Co-Pilot itself grants only +1 gives an indication as to how often the bonus is expected to be used, and the defense roll will be made exactly as often.
In any case, that's just my opinion. Do as you wish at your table.