In the best of circumstances, co-parenting might be a challenge. This is compounded exponentially when your ex is a narcissist. Individuals who have this mental health condition aren't able to compromise like everyone else. They don't understand anything but getting their own way in everything. This presents a problem because neither parent always gets their way in child custody matters.
A person who has a narcissistic ex will wind up sucked into a vacuum of negativity if they don't take protective steps. One of the most important things you can do is to set firm boundaries for the custody matters. Don't allow those to be crossed.
In some cases, holding firm might require that you minimize contact with your ex. This is a tactic that reduces the opportunity for them to try to engage in psychological warfare. This can protect you, but it also protects your child because they won't be subjected to the constant battles between you and your combative ex.
When you do have to deal with your narcissistic ex, remain as unemotional as possible. One of the things that fuels the narcissism is getting a reaction out of their victims. Instead of giving them that satisfaction, remain calm and neutral. They might become angry, but you didn't provide them with the satisfaction of having a negative impact on you.
Having a firm parenting plan in place can also help in these situations. Be sure to think carefully about the terms as you make each decision. The narcissist will likely look for every opportunity to battle with your in court.