Hi Shelly,
I actually am having the exact same problem myself. I was looking for resort options during those dates and have found many locations unavailable.
A few options include, if you are able, adjusting your travel dates slightly. Sometimes by having thre flexibility to arrive just one day earlier or later, you may find rooms available. Also continue to call back often. Cancellations are common at Disney World due to changes in guests' vacation plans so something could open up at anytime. You may want to check with an authorized Disney World travel agents like
www.smallworldvacations.com or
www.mousefantravel.com. They may have access to information on openings through their system, especially if they know one of their clients cancelled a vacation.
Lastly, even if your heart was set on a monorail resort, don't forget there are a number of other Disney resorts that offer similar advantages of proximity to a park. Wilderness Lodge and Fort Wilderness are just a short boat ride away from the Magic Kingdom and you could then hop on the monorail towards Epcot if you would like. The Epcot resort area features the Boardwalk and Yacht and Beach Club, and although it is not the monorail, these locations are within a short boat ride or walk to both Epcot and Hollywood Studios.
Good luck and I hope you find the perfect match for your family!