What do you say when people ask for prayers?

Someone asks for prayers for a friend or family member who is sick. I find myself fumbling for the right answer every time this happens.

I don’t know that I believe in God, so I do not feel right telling them I will keep them in my prayers; however, I feel like saying that I will keep them in my thoughts is kind of an obvious cop-out and not nearly as meaningful to them.

They are the ones who need comfort – should I just go with it for their sake or should I stand by my beliefs (or lack thereof)?

Considering the area I live, it is likely assumed that I am Christian. I don’t discuss religion, or my personal beliefs, with many people – even some close friends and family members are unaware of my thoughts on the subject. It is not because I am ashamed; it is because it is personal and I don’t care to debate or defend my private beliefs.