Check corporate housing and temporary housing websites. They help business people relocate into temporary furnished housing.
Another risky option is Craigslist. You may be able to sublet an apartment.
Try calling a few real estate agencies near Disney. They may know of houses that are for sale that could be rented.
I've lucked into good deals by catching a new listing on VRBO, Homeaway or Flipkey. Nothing was booked yet so I was able to get my dates at a negotiated lower price.
Celebration has a lot of carriage houses. They are often available since they have a 30 day minimum rental period. Start by calling real estate agents there.