The Collaborative International Dictionary of English v.0.48:

Staidness \Staid"ness\, n.
   The quality or state of being staid; seriousness; steadiness;
   sedateness; regularity; -- the opposite of wildness, or
   levity.
   [1913 Webster]

         If sometimes he appears too gay, yet a secret
         gracefulness of youth accompanies his writings, though
         the staidness and sobriety of age be wanting. --Dryden.
   [1913 Webster]

   Syn: Sobriety; gravity; steadiness; regularity; constancy;
        firmness; stability; sedateness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

staidness
    n 1: a trait of dignified seriousness [syn: sedateness,
         staidness, solemnity, solemness]