Personally, as a coffee lover, coffee stains on mugs are not really a big problem that I have. Maybe it’s because I use instant coffee, or because I’m blind and I haven’t noticed the stains yet. Either way, if coffee stains in mugs are a big problem for you, The Kitchn’s Ever Meister might be of help!
Meister tested five different methods for clearing said stains in order to find out the most effective way. Check the results of her experiment here!
Image credit: Sarah Crowley
Otherwise, I use two cups over and over, one for coffee, one for tea, and wash them about once a week when I do dishes. That's a benefit of living alone, and not using milk or sugar in my drinks.