The Collaborative International Dictionary of English v.0.48:

Harmonious \Har*mo"ni*ous\ (h[aum]r*m[=o]"n[i^]*[u^]s), a. [Cf.
   F. harmonieux. See Harmony.]
   1. Adapted to each other; having parts proportioned to each
      other; symmetrical.
      [1913 Webster]

            God hath made the intellectual world harmonious and
            beautiful without us.                 --Locke.
      [1913 Webster]

   2. Acting together to a common end; agreeing in action or
      feeling; living in peace and friendship; as, an harmonious
      family.
      [1913 Webster]

   3. Vocally or musically concordant; agreeably consonant;
      symphonious. -- Har*mo"ni*ous*ly, adv. --
      Har*mo"ni*ous*ness, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

harmoniously
    adv 1: in a harmonious manner; "the problem of absorbing
           immigrants harmoniously into British society is as
           important to the immigrants as to the British"

Moby Thesaurus II by Grady Ward, 1.0:

41 Moby Thesaurus words for "harmoniously":
   agreeably, as one, as one man, back to back, by consensus,
   coactively, coefficiently, collectively, combinedly, communally,
   compatibly, concertedly, concordantly, concurrently, congenially,
   conjointly, consonantly, cooperatingly, cooperatively, fittingly,
   hand in glove, hand in hand, in chorus, in concert,
   in concert with, in keeping, in line, in step, in unison, jointly,
   just right, like clockwork, methodically, regularly,
   shoulder to shoulder, systematically, together, unanimously,
   uniformly, with it, with one voice