Hello, Teresa,
I checked the list of amenities for the Little Mermaid standard rooms, and a coffee maker is not included. However, you are certainly welcome to call housekeeping upon your arrival to see if there would be an extra one available that you could use during your stay, but there aren't any guarantees with this option.
I did research the option of renting a coffee maker for another guest, and I wasn't able to locate a business that offered this. However, some guests opt to purchase an inexpensive coffee maker to stow away in their luggage or purchase upon arrival. Then rather than have it take up valuable room in their luggage for the return trip, they just leave it in the room.
Just an fyi, the Landscapes of Flavor (the counter service restaurant at the resort) does have iced mochas, cappuccinos, and espresso on the menu, which count as snack items if you are on the Disney Dining Plan. You can also purchase a refillable mug for free coffee at your resort throughout your trip.
And did you know
Starbucks is headed to the parks? You can also read about some of my other favorite coffee spots
here.
Have a great trip and enjoy Disney's Art of Animation; it is an amazing resort! Please let us know if you have any more questions.