That you are about two months too late.
All of the restuarants start accepting reservations 180 days out. The ones with buffets and/or characters tend to get sold out the fastest. The end of June is getting fairly crowded.
Basically your only chance for a reservation for a group that size is within 30 minutes of the time a restaurant opens or within 30 minutes of the last reservations accepted.
I belong to a group that has an annual Holiday Dinner at WDW in December. We have already decided where we will hold this year, and will talk to the manager of the restaurant to hold a block of 50 seats for us at opening on that date. We can then fine-tune the reservation. But they will keep 50 seats as unavailable for the first two hours from opening in the reservations system.