The Collaborative International Dictionary of English v.0.48:

Perversely \Per*verse"ly\, adv.
   In a perverse manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

perversely
    adv 1: deliberately deviant; "his perversely erotic notions"
    2: in a contrary disobedient manner [syn: perversely,
       contrarily, contrariwise]

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "perversely":
   bearishly, cantankerously, churlishly, contrarily, contrariwise,
   crabbedly, crankily, crossly, crustily, fractiously, frowardly,
   huffily, ill-humoredly, ill-naturedly, irascibly, irritably,
   snappily, sourly, sulkily, sullenly, testily, waywardly,
   wrongheadedly