The Collaborative International Dictionary of English v.0.48:

Sedulous \Sed"u*lous\ (?; 135), a. [L. sedulus, perhaps from
   sedere to sit, and so akin to E. sit.]
   Diligent in application or pursuit; constant, steady, and
   persevering in business, or in endeavors to effect an object;
   steadily industrious; assiduous; as, the sedulous bee.
   [1913 Webster]

         What signifies the sound of words in prayer, without
         the affection of the heart, and a sedulous application
         of the proper means that may naturally lead us to such
         an end?                                  --L'Estrange.
   [1913 Webster]

   Syn: Assiduous; diligent; industrious; laborious;
        unremitting; untiring; unwearied; persevering.
        [1913 Webster] -- Sed"u*lous*ly, adv. --
        Sed"u*lous*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

sedulously
    adv 1: in a sedulous manner; "this illusion has been sedulously
           fostered"