Your relative with cancer needs your love and support. That doesn't mean you bring up the topic and try to discuss it in detail. It means that you are there, for that person, in a loving way, looking for moments of enjoyment and encouragement.
A person with cancer goes through several emotional stages. (See Elisabeth Kubler-Ross' book on Death and Dying.) The first is numbness and denial. The second may be grief (tears). The third may be anger. This may be followed by bargaining (God, give me another year or heal me and my life will be different.) The final stage will be acceptance of the situation or rejection and depression.
A person can go back and forth among these stages. Just be there to be loving, no matter what the stage. Take each moment you have with this person as precious, and do something, as you can, to make it special. That can be an ice cream cone, watching a comedy DVD, looking at photos. Small things that bring enjoyment are very big during such a time.
A lot of prayer on your part will be helpful, too. Ask people at your church to be praying for your family member. God has the power to step in and make things happen when we think it's totally impossible.
I hope this has been helpful. As someone who's been through cancer and survived, I know fully how vital it is to have the love and support and thoughtfulness of those around you.