Why a duke? "It's traditional," says Charles Kidd, editor of Debrett's Peerage and Baronetage. Kidd has surveyed the most likely candidates among the currently vacant titles, including a few with a less than enticing history:
CAMBRIDGE - The second Duke of Cambridge, Prince Adolphus Frederick, was the seventh son of King George III. Defying the Royal Marriage Act, he married his mistress, Sarah Louisa Fairbrother, an actress and a commoner, in 1847. Since the marriage wasn't legal, his children were all illegitimate.
SUSSEX - Conferred upon Prince August, sixth son of King George III, in 1801. Neither of his two marriages were recognized by the king, and the title lapsed at his death in 1843.
CONNAUGHT and STRATHEARN - Conferred upon Prince Arthur, third son of Queen Victoria in 1867. He died in 1942, and was succeeded by his grandson, Alastair, second Duke of Connaught and Strathearn, who died on active service in 1943.
CLARENCE and AVONDALE - The Dukedom of Clarence dates to the 14th century, when the title was given to Lionel of Antwerp, third son of King Edward III. Prince Albert Victor, a grandson of Queen Victoria, was created Duke of Clarence and Avondale in 1890. He died unmarried two years later.
However, Kidd notes, Queen Elizabeth II could also create a new title for William.