Hello, Wendy,
At the Animal Kingdom Lodge, you'll find that the coffee is Nescafe from the big machines. You'll find cream, sugar, and sugar substitutes available to you as well, but no other coffee drinks.
To have other coffee options, there are other java spots throughout Walt Disney World (but your refillable mug won't work there), and my favorite is the Kona Cafe at the Polynesian Resort (Shhhh, I have to confess that sometimes after arriving at the Magic Kingdom I opt to go straight onto the monorail to slip over there for a cup of Kona coffee).
To see a complete list of coffee options, you'll want to visit www.allearsnet.com and do a search for
Real Coffee.
Also, you will have a coffee maker in your room, so don't hesitate to bring your own favorite brew if you'd prefer that.
By the way, if your trip isn't in the immediate future,
Starbucks is headed to Walt Disney World!