Hi, CC. I agree with morning_after about focusing on the present and asking how your cousin is at the moment. And if the subject of her cancer does come up, approaching it in a matter of fact, logical, manner is really the best way to deal with it. I can tell you this as a patient in hospital who was facing the possibility of passing away.
I found my favorite visitors were the ones that treated me like I was the same person I was before I was so ill. They came in, they talked to me about what was going on in the world, how I was feeling at the time. We talked about them, as well. When they did ask questions about my illness or hospital stay they were rational, and non-emotional questions that I could answer with facts. The ones that came in with that tone of pity that just drips from a person's words drove me crazy and I wanted them to leave 2 minutes after they arrived. I prefered the angry "I hate that this could happen to you!" to "You poor thing. And your poor children..."
I wanted to smack 'em.
Even though doctors may say there is "X' amount of time before someone passes away, they usually don't want to be reminded or treated that way. It's hard to stay alive when people are treating you like you're already dead.
Hope my perspective helps.
Luv ya,
Lauri