Hi Carrie,
What a fantastic idea your children had to celebrate their Birthday's, I'd always choose a trip to Disney instead of a party too :-)
You can certainly book an advanced dining reservation for 1 night of your stay only. There are many character restaurants to choose from so I would recommend you visit
allears select dining and then on the left hand side there is a link to character meals. This will list all the restaurants and which characters are normally there. My families personal favourites are Crystal Palace at the Magic Kingdom, 1900 Park Fare at the Grand Floridian and Akershus at Epcot. You could even involve your children in the planning unless you'd like to keep it a surprise.
For the best chance of securing the reservation you want I suggest you call 407-939-3463 as soon as you get to 90-days before your arrival date.
Are you actually in WDW for one of your children's birthdays? If so they can receive a special birthday present, click
HERE for details and to sign up.
Have a great trip and feel free to ask us any more questions you may have,
Jo