It's very difficult to know what to say in these situations when they have a different belief system. Sometimes by just being there for them and feeling Compassion for them helps them not to feel threatened by you. Often when people die other people feel so uncomfortable with the relatives of those who died because of their grief that they don't know what to say or do, so they stay away. But it's important not to stay away through our sense of not wishing to open to their pain.
However, if they are truly Christians, then we could focus on and talk about the good qualities of the relative and if they really do believe in Christian principles, then hoping that they are well wherever they are. Which goes into Compassionate/Lovingkindness for the person who is gone. It depends on whether they are ready for it though. So you have to be very sensitive to what the person is saying and listen to them first, so that you can first feel with them, be okay with their grief. Let them lead you into knowing what is correct to say.