The Collaborative International Dictionary of English v.0.48:

Regularly \Reg"u*lar*ly\, adv.
   In a regular manner; in uniform order; methodically; in due
   order or time.
   [1913 Webster]

WordNet (r) 3.0 (2006):

regularly
    adv 1: in a regular manner; "letters arrived regularly from his
           children" [syn: regularly, on a regular basis] [ant:
           irregularly, on an irregular basis]
    2: having a regular form; "regularly shaped objects" [ant:
       irregularly]
    3: in a regular way without variation; "try to breathe evenly"
       [ant: irregularly]

Moby Thesaurus II by Grady Ward, 1.0:

78 Moby Thesaurus words for "regularly":
   always, as a rule, as per usual, as things go, as usual,
   at all times, at every turn, at regular intervals, at stated times,
   ceaselessly, chiefly, chronically, commonly, constantly,
   continually, customarily, daily, daily and hourly, day after day,
   day and night, evenly, ever, ever and anon, every day, every hour,
   every moment, every so often, frequently, generally, habitually,
   harmoniously, hour after hour, hourly, incessantly, intermittently,
   invariably, inveterately, like clockwork, mainly, methodically,
   month after month, most often, mostly, naturally, never otherwise,
   night and day, normally, normatively, on and on, on wheels,
   orderly, ordinarily, perennially, perpetually, persistently,
   prescriptively, punctually, rapidly, recurringly, repetitively,
   right along, routinely, smoothly, steadily, sustainedly,
   systematically, to be expected, unceasingly, uniformly,
   unintermittently, uninterruptedly, unvaryingly, usually,
   without cease, without exception, without letup, without stopping,
   year after year