Welcome aboard, Jacqueline! You'll be setting sail on your eighth Disney cruise? You must have learned early on that Disney Cruise Line is very special, and it is certainly a magical place to celebrate your children's birthdays!
Those wonderful circular booth tables in
Enchanted Garden are referred to as "teacup tables" by the servers, which seems very fitting, doesn't it? Though Disney Cruise Line cannot guarantee it, you will have a good shot at being assigned one of those tables if you put in a call to your travel agent or Disney Cruise Line and make that request on your reservation.
Since you've sailed many times before, you probably know that you can also request certain dining servers or a certain dining rotation. However, if you do that, you will have much less chance of getting one of the teacup tables. I'd suggest making the teacup request your only dining request to have a better chance of being assigned to one of those great spots.
I wish your family a very magical cruise, and a very happy birthday to both of your children! Please let me know if I can help you with any other questions before you set sail!