I am the queen of inappropriate comments in tough situations. I do it to get a giggle out of those affected by the situation.
I'll try to think back to a funny moment, a story/anecdote the coworker would have shared and talk about that. Maybe throw in something else that happened at work (like "(blank) was pretending to be a walrus with the coffee stirrers and they actually got stuck!" etc.)
If she was really close, I say something to get the "are you serious face?" which is usually followed by a smile. (EX: cracks about the hospital gowns or something to induce a little giggle) If that didn't work, I'd probably ask if my shoes made my feet look big/fat - just to throw them off-guard - ANYTHING to distract the mind.
Show concern, ask her for updates, and ask if there is anything you could do to help. Offerings of meals are huge at a time like this. But if you aren't comfortable preparing a meal, maybe take up a collection at work to buy her some gift cards (food, gas cards, drink cards, etc) to use while she's at the hospital. Maybe find her a book to read that is in high spirits, nothing heavy or sad. Bring/send a small bundle of flowers to her to let her know you guys are thinking of her and sending massive good thoughts to her daughter.
Best of luck and please keep us posted with updates!