Grout is porous, so the coffee stains aren't so much ON the grout as IN the grout -- and could go pretty deep. I'm guessing one of the bleaches will work -- either H2O2 or chlorine (diluted a lot!). I'd rig up a way for the bleach to sit there for a while -- half an hour or more. Depending on how large an area you're cleaning I'd start with the H2O2 because it's safer -- unless your area is really large then I'd say just go straight to the chlorine because it's a lot cheaper. Don't get your face right over the chlorine, especially when pouring or diluting.

This is assuming the tiles are not porous, so they won't get bleached out too.

Now you just have to decide whose advice to take!

O..O
=o=