When a close friend or family member is "asking for prayers" and you want to wish them well what should you say?
I might just say, I’ll pray for you. They don’t need to know I’m fibbing.
"My heart is open for you/them/[whatever]. I will be honored to bear witness to your/their suffering."
For me, it depends where they live. If they live close enough to me, I'll let them know I'm here if they need help, a babysitter, to go out and just get a drink and relax, or a shoulder to cry on or an ear to bend. If they live far away, I'll let them know that I'm available to listen to their worries and be whatever help I can anytime.
I currently have a situation like that in my life right now. An actor friend who lives in LA, whom I've known literally since the first month I moved to Memphis and we went to the same schools until we graduated high school together, has a child with a type of cancer. They caught it sort of early, but it's still taking quite a toll on the boy, and as he and his wife and their family are religious they have asked for prayers in their FB posts. One thing that a few of us suggested was a fundraiser for the incredible expenses associated with cancer that many don't think about such as simple bill money, grocery money, gas, and even the extra medical expenses. I mean he's an actor and if he's not actually in a movie or on a tv show, he's really not making any money right then and taking out of savings or what have you. His wife has taken a leave of absence to care for their kid, and it's an incredible emotional toll even before money gets involved. He has a friend, Bill Burr, who decided to put on a fundraising show for him and his family, and a donations page was set up as well. So, long story short (too late I know lol) there is always something that can be done that doesn't have anything to do with anyone's beliefs beyond empathy, compassion, and love for their friends and family.
Sorry for the wall of text there...
I've never had anyone confront me to ask for prayers, so it's always been more along the lines of Facebook posts and so forth. If they're not terribly close to me, relationship-wise, I just ignore those requests. If I know them well, I'll say something to indicate that I'm thinking about them and hoping for the best. If they're especially close friends or family and physically close, I'll ask what I can do to ease their burden.
I say "I'm sending you all my positive thoughts and good intentions your way". I've never asked how this has been received but I assume that they take it in the same way I do when they say they're praying for for me: That they're trying to be supportive.