Go to the area in the afternoon on the first day that does dining changes (it is in one of the bars, like where Palo reservations are made).
Bring your table number (which you will find in your room). Have them check to see if you are at a table just for 4. If not, have them check to see if they can find you one.
We are also a family that wants a table for 4, and so far we have been able to get one each time. This upcoming cruise we have lots of friends joining us, so there will actually be 14 of us this time and it is going to be quite different! A new experience!
DJ