I know that the villas have coffee pots, you have to pay if you use their coffee, so, I bring my own so that I have at least a few good cups of coffee in the morning! Everything else is hit or miss throughout the day, depending upon where you eat!
kona,boma, and narcosses all have press pot coffee
The ground coffee for sale in the AKL gift shop is fantastic... I usually buy that and brew it in my room. It's Kenyan coffee roasted by Joffrey's, but it's in an "exclusive for AKL" package.