The late Queen's issued the most Family Orders in the year of her accession, 1952. The following received theirs then:
The Queen Mother
Princess Margaret
Queen Mary
Princess Mary, Princess Royal
Princess Alice, Duchess of Gloucester
Princess Alice, Countess of Athlone
Princess Marina, Duchess of Kent
After that it was issued in the following years to:
1961 - The Duchess of Kent
1969 - The Princess Royal
1973 - The Duchess of Gloucester
1981 - Diana, Princess of Wales
2004 - The Duchess of Edinburgh
2007 - Queen Camilla
2017 - The Princess of Wales
Of the remaining female family members I can see the Queen, Princess of Wales and Duchess of Edinburgh and the Princess Royal being the most likely recipients of the King's Family Order. It may be this year they will receive it or next year. The Duchess of Gloucester and Princess Alexandra may receive it for the loyality they showed his mother and him. I can't see the York Princesses or Lady Louise receiving it.
There is the matter of when Princess Alexandra received hers because she did wear it for the 1953 coronation.
Link to RJWMB for pic.
The matter of seven made initially but eight recipients has been discussed on the
History of Famous Jewels and Collections
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