The Collaborative International Dictionary of English v.0.48:

Keenly \Keen"ly\, adv.
   In a keen manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

keenly
    adv 1: in a keen and discriminating manner; "he was keenly aware
           of his own shortcomings"

Moby Thesaurus II by Grady Ward, 1.0:

70 Moby Thesaurus words for "keenly":
   acerbically, acerbly, acidly, acridly, acrimoniously, actively,
   animatedly, anxiously, ardently, avidly, bitingly, bitterly,
   breathlessly, briskly, caustically, con brio, cordially,
   corrodingly, corrosively, cuttingly, eagerly, energetically,
   enthusiastically, excitedly, exuberantly, fervently, fervidly,
   forcefully, forcibly, glowingly, hardly, heart and soul, heartily,
   heatedly, impassionedly, impatiently, incisively, intensely,
   kindly, lustily, mordaciously, mordantly, passionately,
   penetratingly, piercingly, promptly, quickly, rancorously, readily,
   scathingly, scorchingly, sharply, sorely, spiritedly, stabbingly,
   strenuously, tartly, trenchantly, vigorously, vivaciously, warmly,
   with alacrity, with gusto, with open arms, with pep, with relish,
   with zest, witheringly, zealously, zestfully