The Collaborative International Dictionary of English v.0.48:
Viscountship \Vis"count`ship\, Viscounty \Vis"count`y\, n. [F. vicomt['e].] The quality, rank, or office of a viscount. [1913 Webster]WordNet (r) 3.0 (2006):
viscounty n 1: the dignity or rank or position of a viscount or viscountess [syn: viscountcy, viscounty] 2: the domain controlled by a viscount or viscountess