Hi William! I tend to be a last-minute planner, so I know how frustrating it can be when you really want to eat at a particular restaurant and can't get a reservation. I'm traveling to Disney World myself this week, and I've been trying to reserve a table at Le Cellier, also in Epcot, for six months. I happened to check availability today and to my surprise, I was finally able to make a reservation for later this week. The key to getting in the Disney restaurant of your choice is persistence and flexibility. Keep checking for available tables as other guests constantly cancel and reschedule their reservations, and be flexible about your dining times. When looking for reservations, check for every day of your trip and consider looking for tables at lunch as well as dinner. (I'm not sure of the size of your party, but I did just check availability of Coral Reef for your travel dates and although dinner was booked up, several lunch seatings were available.) If you're unable to reserve a table in advance, you can always try walking up to Coral Reef -- if other guests fail to appear for their reservations, you may be able to get a table.
Coral Reef has a cool, tranquil atmosphere; it's so relaxing to watch the fish swimming in the giant aquariums while you dine. However, if you're unable to dine there, consider Rose & Crown, Le Cellier, Via Napoli, or Teppan Edo instead. Although those Epcot restaurants don't have the same wonderful underseas atmosphere as Coral Reef, they have food that, in my opinion, is even more delicious than Coral Reef.
Hope this helps! Come visit us again the Moms Panel if you have more questions!