The Collaborative International Dictionary of English v.0.48:

Contrarily \Con"tra*ri*ly\ (? or ?), adv.
   In a contrary manner; in opposition; on the other side; in
   opposite ways.
   [1913 Webster]

WordNet (r) 3.0 (2006):

contrarily
    adv 1: in a contrary disobedient manner [syn: perversely,
           contrarily, contrariwise]
    2: contrary to expectations; "he didn't stay home; on the
       contrary, he went out with his friends" [syn: contrarily,
       to the contrary, contrariwise, on the contrary]