The Collaborative International Dictionary of English v.0.48:

Unvarying \Unvarying\
   See varying.

WordNet (r) 3.0 (2006):

unvarying
    adj 1: unvarying in nature; "maintained a constant temperature";
           "principles of unvarying validity" [syn: changeless,
           constant, invariant, unvarying]
    2: lacking variety [syn: unvaried, unvarying] [ant:
       varied]
    3: always the same; showing a single form or character in all
       occurrences; "a street of uniform tall white buildings" [syn:
       uniform, unvarying] [ant: multiform]

Moby Thesaurus II by Grady Ward, 1.0:

132 Moby Thesaurus words for "unvarying":
   abiding, accordant, alike, automatic, balanced, blah,
   broken-record, ceaseless, changeless, chattering, consistent,
   consonant, constant, continual, continuing, continuous,
   correspondent, drearisome, dreary, dry, dryasdust, dull, durable,
   dusty, enduring, equable, equal, even, everlasting, firm, fixed,
   flat, frozen, harping, homogeneous, humdrum, immobile, immutable,
   incessant, incommutable, inconvertible, indefeasible, inert,
   insusceptible of change, intact, intransmutable, invariable,
   inviolate, irretrievable, irreversible, irrevocable, jog-trot,
   lasting, level, long-winded, machine gun, measured, mechanical,
   methodic, monolithic, monotonous, noble, nonreturnable,
   nonreversible, of a piece, ordered, orderly, oscillating,
   perennial, permanent, perpetual, persistent, prolix, pulsating,
   quiescent, rapid, regular, remaining, repeated, reverseless, rigid,
   robotlike, singsong, smooth, solid, stabile, stable, staccato,
   static, stationary, staying, steadfast, steady, stuttering,
   sustained, systematic, tedious, torpid, treadmill, unalterable,
   unalterative, unaltered, unbroken, unceasing, unchangeable,
   unchanged, unchanging, unchecked, undeflectable, undestroyed,
   undeviating, undifferentiated, undiversified, uneventful, unfading,
   unfailing, uniform, unintermitted, unintermittent, unintermitting,
   uninterrupted, unmodifiable, unremitting, unrestorable,
   unreturnable, unruffled, unshifting, unstopped, unsusceptible,
   unvariable, unvaried, vibrating