If you want to know how to coParent with a narcissist, first make sure you are actually dealing with a “real” and not perceived narcissist.
If in fact, you are dealing with a genuine case of narcissism, then the best course of action will in all likelihood would be intervention, usage of a third party neutral, mediation and counseling. There will also be a lot of very hard work by each party in order to transcend the disorder or illness and be child centered in your coParenting.
If you want to learn how to coParent with a really difficult person that is a pony with different stripes… First, don’t add fuel to the fire by being a name caller. Take a step away from the conflict in order to access the best use of your emotional, financial and physical resources. Once you have taken inventory or stock of your life, then you are better equipped to let the things that really don’t matter to you slide. Why incite a fight when it is something that you may not really care about?
Next, slowly perhaps but with deliberateness you begin to communicate in small bits of information or requests. When your coParent is responsive, the outcome is positive. Not because you got your way but because it is a child centered approach.
Praise your coParenter with sincerity. Expand the dialog over time and consider inviting a third party who is neutral to assist you and your coParenter to be able to sort through decision making without running back to court.
Whatever you do, don’t call names or affix false labels. Bones may not be broken but words can sting and are incendiary, capable of burning up every hope or expectation of child centric decision making.