Instead of asking "How are you doing?", ask "How are you grieving?"
This makes far more sense to me as a recovering griever. Whenever someone asked "How are you doing?" -- and I could even be crying when they asked -- I'd always stop mid-blubber and stare at them slack-jawed. Like I'd been slapped. HARD.
My internal responses were: "What the fuck do you think?! [insert irreverent name based on gender]", or a more generic - yet not quite vanilla - "I feel like shit. Duh."
Instead, out loud, I resorted to "Fine" or a shrug with a trailing off "Well ..." or "You know ..." Embarrassed-like.
And then I'd feel even more shitty for suggesting that I was "Fine" that my husband had just died, and I felt like throwing up in my mouth a little bit.
Seriously. Don't put grievers in that situation.
What you really want to know anyway is how they are grieving. Do they stare at the wall? Are they sleeping? Can they eat yet?
Ask those questions.