If you are willing to splurge for a night, the chef's table at Victoria and Albert's is the place to be. According to the general manager there, they average 2 engagements a night and in their years of operation, they have never had anyone say 'no' to a proposal at their chef's table.
Book WAY in advance for that, though.
Also, the Grand Floridian, Contemporary and I believe AKL and Polynesian offer a special balcony for 'room service', but the meal is entirely created especially for the guests. Again, booking way ahead of time is key with Disney engagements.
IF you are at the Grand Floridian, be sure to speak with dining services to have them bring the ring on the glass slipper plate. (This is a beautiful white chocolate slipper like that of Cinderella that has raspberry mousse inside, and they will place your ringbox next to it and remove the silver cover at the table). HIGHLY RECOMMENDED.
If you want to do it at the Living Seas for whatever reason, they can arrange for a diver to swim with a sign labeled "will you marry me" down to your table. The waiters and waitrsses will notify the rest of the restaurant secretly and when she says yes, everyone will stand and cheer.
CALL IN ADVANCE. TRUST ME. They can do anything, ANYTHING, you want for them, save maybe graffiti on the castle. But your wish is their command, as long as you give ample notice!