Antipater .

Wagner, Sir Anthony Richard; ‘Pedigree and Progress: Essays in the Genealogical Interpretation of History’ puts this Antipater as the son of Salome and Joseph.

Tal Ilan, in the Jewish Women's Archives puts him as the son of Salome and Costobarus http://jwa.org/encyclopedia/article/salome

If anybody has more sources or opinions, I've opened a Discussion on which father we should choose here. For the moment Tal Illan's article seems very well researched, and potentially more up to date than Wagner, who is occasionally wrong in this area, so I've gone with Costobarus. [Sharon April 2012]