I believe that the two quietest times of year are meant to be immediately after Thanksgiving (very end Nov- early Dec) and immediately after Presidents Day (late Feb).
However, Disney is pretty incredible at making itself busy all year round, and just because those are the quietest times may not mean they are cheaper. You may just find that there are some extra offers around EG free dining offers or ticket extensions.
Do a few searches on the room booking site and see if you can spot any dips in prices - I would think that if they exist they may be straight after American public holidays.
Good luck!
Miranda