There was a coffee pot in our room both times we stayed at CBR. If there isn't one in your room when you check in, you can call Housekeeping to request one.
Last year at CBR we had a 4-cup coffeemaker. The coffee packets were $1 each. We didn't use it for coffee (had refillable mugs 2 minutes from food court) but had teabags, chai, etc. and instant oatmeal that we brought.
CSR has coffee makers in everyroom along with coffee paskets. They will refill the coffee supply daily. You can request a coffee maker at any WDW resort. Bring you own coffee in a small container if you don't stay at CSR!