I’m sorry @seasonswithmsjm, but I, too, have not had someone close to me pass away, much less a non-believer. I have, however, experienced the grieving of others (believers and non-believers) through my work at a local hospital and, recently through the deaths of two young women and the mother of a close friend in my personal circle. I do not have any definitive answers but what I have learned and am learning is first and foremost to be with the person who is grieving. It is uncomfortable for most of us not to talk, but sometimes just sitting with the person as they cry is enough. Letting them know that they are not alone and they have your full attention can be powerful. I recently asked whether I could pray for a non-Christian colleague and her family member who is very ill and not expected to live.
My colleague was so grateful.
On the other hand I recently listened to an interview on Premier Christian radio where the person being interviewed had lost his wife and was admonishing listeners that saying “there are no words” is unhelpful and essentially a cop-out. The brief snippet is here.
I think that no matter what you do, be present with the grieving individual. Be patient with them. Grieving takes time. By loving them through their grief you will be “Jesus with skin on” as the saying goes. Be attentive to the leading of the Holy Spirit as to what to say and when. The grieving person may reach out to you and then you can share the reason for the hope that you have. Remember that God is big enough to handle our anger.
May God grant you wisdom and encourage you as you journey together with the people in your life who suffer through grief.