The Collaborative International Dictionary of English v.0.48:

Happily \Hap"pi*ly\ (h[a^]p"p[i^]*l[y^]), adv. [From Happy.]
   1. By chance; peradventure; haply. [Obs.] --Piers Plowman.
      [1913 Webster]

   2. By good fortune; fortunately; luckily.
      [1913 Webster]

            Preferred by conquest, happily o'erthrown. --Waller.
      [1913 Webster]

   3. In a happy manner or state; in happy circumstances; as, he
      lived happily with his wife.
      [1913 Webster]

   4. With address or dexterity; gracefully; felicitously; in a
      manner to insure success; with success.
      [1913 Webster]

            Formed by thy converse, happily to steer
            From grave to gay, from lively to severe. --Pope.

   Syn: Fortunately; luckily; successfully; prosperously;
        contentedly; dexterously; felicitously.
        [1913 Webster]

WordNet (r) 3.0 (2006):

happily
    adv 1: in a joyous manner; "they shouted happily" [syn:
           happily, merrily, mirthfully, gayly, blithely,
           jubilantly] [ant: unhappily]
    2: in an unexpectedly lucky way; "happily he was not injured"
       [ant: sadly, unhappily]

Moby Thesaurus II by Grady Ward, 1.0:

43 Moby Thesaurus words for "happily":
   agreeably, airily, blessedly, blissfully, blithely, cheerfully,
   cheerily, delightedly, ecstatically, elatedly, enthusiastically,
   exultantly, favorably, fortunately, gaily, genially, gladly,
   gleefully, heartily, hopefully, irrepressibly, jauntily, joyfully,
   jubilantly, lightly, luckily, merrily, opportunely, optimistically,
   peaceably, pleasantly, propitiously, prosperously, providentially,
   rapturously, rhapsodically, satisfyingly, smilingly, successfully,
   swimmingly, willingly, with good cheer, with pleasure



The Jargon File (version 4.4.7, 29 Dec 2003):

happily
 adv.

    Of software, used to emphasize that a program is unaware of some important
    fact about its environment, either because it has been fooled into
    believing a lie, or because it doesn't care. The sense of ?happy? here is
    not that of elation, but rather that of blissful ignorance. ?The program
    continues to run, happily unaware that its output is going to /dev/null.?
    Also used to suggest that a program or device would really rather be doing
    something destructive, and is being given an opportunity to do so. ?If you
    enter an O here instead of a zero, the program will happily erase all your
    data.? Nevertheless, use of this term implies a basically benign attitude
    towards the program: It didn't mean any harm, it was just eager to do its
    job. We'd like to be angry at it but we shouldn't, we should try to
    understand it instead. The adjective ?cheerfully? is often used in exactly
    the same way.


The Free On-line Dictionary of Computing (30 December 2018):

happily

   Of software, used to emphasise that a program is unaware of
   some important fact about its environment, either because it
   has been fooled into believing a lie, or because it doesn't
   care.  The sense of "happy" here is not that of elation, but
   rather that of blissful ignorance.  "The program continues to
   run, happily unaware that its output is going to /dev/null."

   [Jargon File]