(remember, NEVER try cleaning them with bleach. Bleach causes pinholes in the steel and wrecks them)
+1 bleach is highly corrosive. To remove coffee stains, I use "softened" water to soak overnight and usually the interior is back to like-new condition the next morning. If the stain is really thick, may take more than one try to get it shiny again. I use powerdered Calgon water softener, but I assume liquid water softener should work equally well. May temporarily leave a floral scent from the water softener.
The water softener tricks works wonders on many baked on stains in pots and pans. I have soaked burnt food for days in plain water--nothing. Still rock hard. But then one night of soaking with the water softener and it slips right off as I pour out the water.