The Collaborative International Dictionary of English v.0.48:

Duly \Du"ly\, adv.
   In a due, fit, or becoming manner; as it (anything) ought to
   be; properly; regularly.
   [1913 Webster]

WordNet (r) 3.0 (2006):

duly
    adv 1: at the proper time; "she was duly apprised of the raise"
           [syn: punctually, duly]

Moby Thesaurus II by Grady Ward, 1.0:

38 Moby Thesaurus words for "duly":
   accordingly, appropriately, as is proper, as is right, by right,
   by rights, condignly, correctly, deservedly, disinterestedly,
   dispassionately, equally, equitably, evenly, fair, fairly,
   fittingly, impartially, impersonally, in all conscience, in reason,
   inequity, injustice, justifiably, justifiedly, justly, meetly,
   on time, properly, punctually, right, rightfully, rightly,
   suitably, upon even terms, warrantably, warrantedly,
   without distinction