The Collaborative International Dictionary of English v.0.48:

Contriteness \Con"trite`ness\, n.
   Deep sorrow and penitence for sin; contrition.
   [1913 Webster]

WordNet (r) 3.0 (2006):

contriteness
    n 1: sorrow for sin arising from fear of damnation [syn:
         attrition, contrition, contriteness]