The Collaborative International Dictionary of English v.0.48:

Earnestly \Ear"nest*ly\, adv.
   In an earnest manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

earnestly
    adv 1: in a serious manner; "talking earnestly with his son";
           "she started studying snakes in earnest"; "a play dealing
           seriously with the question of divorce" [syn:
           seriously, earnestly, in earnest]

Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "earnestly":
   actively, ardently, assiduously, bec et ongles, committedly,
   decidedly, decisively, decorously, demurely, determinedly,
   devotedly, devoutly, dingdong, down, exhaustively, fervently,
   fervidly, firmly, fixedly, for real, formally, gravely, grimly,
   hammer and tongs, heart and soul, heartily, heatedly,
   impassionedly, in all seriousness, in earnest, in good earnest,
   inflexibly, intensely, intently, like a bulldog, like a leech,
   obstinately, painstakingly, passionately, perfervidly,
   perseveringly, persistently, purposefully, relentlessly,
   resolutely, resolvedly, sedately, seriously, sincerely,
   singlemindedly, sober-mindedly, soberly, sobersidedly, solemnly,
   somberly, staidly, staunchly, steadfastly, steadily, tenaciously,
   thoroughly, thoughtfully, tooth and nail, unremittingly,
   unswervingly, unyieldingly, vehemently, wholeheartedly,
   with a will, with constancy, with total dedication, zealously