The Collaborative International Dictionary of English v.0.48:

Constitutionally \Con`sti*tu"tion*al*ly\, adv.
   1. In accordance with the constitution or natural disposition
      of the mind or body; naturally; as, he was
      constitutionally timid.
      [1913 Webster]

            The English were constitutionally humane. --Hallam.
      [1913 Webster]

   2. In accordance with the constitution or fundamental law;
      legally; as, he was not constitutionally appointed.
      [1913 Webster]

            Nothing would indue them to acknowledge that [such]
            an assembly . . . was constitutionally a Parliament.
                                                  --Macaulay.
      [1913 Webster]

WordNet (r) 3.0 (2006):

constitutionally
    adv 1: according to the constitution; "this was constitutionally
           ruled out" [ant: unconstitutionally]