The Collaborative International Dictionary of English v.0.48:

Managership \Man"a*ger*ship\, n.
   The office or position of a manager.
   [1913 Webster]

WordNet (r) 3.0 (2006):

managership
    n 1: the position of manager

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "managership":
   captainship, chairmanship, convenership, custody, dictatorship,
   directorate, directorship, foremanship, generalship, governorship,
   guardianship, headship, intendancy, leadership, mastership,
   overseership, presidency, proctorship, sovereignty, stewardship,
   superintendence, superintendency, supervisorship