The Collaborative International Dictionary of English v.0.48:

Stability \Sta*bil"i*ty\ (st[.a]*b[i^]l"[i^]*t[y^]), n. [L.
   stabilitas; cf. F. stabilit['e]. See Stable, a.]
   1. The state or quality of being stable, or firm; steadiness;
      stableness; firmness; strength to stand without being
      moved or overthrown; as, the stability of a structure; the
      stability of a throne or a constitution.
      [1913 Webster]

   2. Steadiness or firmness of character; firmness of
      resolution or purpose; the quality opposite to
      fickleness, irresolution, or inconstancy; constancy;
      steadfastness; as, a man of little stability, or of
      unusual stability.
      [1913 Webster]

   3. Fixedness; -- as opposed to fluidity.
      [1913 Webster]

            Since fluidness and stability are contrary
            qualities.                            --Boyle.
      [1913 Webster]

   Syn: Steadiness; stableness; constancy; immovability;
        firmness.
        [1913 Webster]

WordNet (r) 3.0 (2006):

stability
    n 1: the quality or attribute of being firm and steadfast [syn:
         stability, stableness] [ant: instability,
         unstableness]
    2: a stable order (especially of society) [ant: instability]
    3: the quality of being enduring and free from change or
       variation; "early mariners relied on the constancy of the
       trade winds" [syn: constancy, stability] [ant:
       changefulness, inconstancy]

Moby Thesaurus II by Grady Ward, 1.0:

226 Moby Thesaurus words for "stability":
   abidingness, abnegation, abstinence, accordance, age, antiquity,
   application, assiduity, assiduousness, authenticity,
   authoritativeness, body, bulldog tenacity, calculability, calm,
   calmness, ceaselessness, changelessness, coeternity, cohesion,
   concentration, concreteness, consecutiveness, conservatism,
   consistency, consonance, constancy, constant flow, constraint,
   continence, continualness, continuance, continuity, continuousness,
   control, cool, correspondence, defeat of time, defiance of time,
   density, dependability, determination, diligence, dispassion,
   diuturnity, dogged perseverance, doggedness, durability,
   durableness, duration, endlessness, endurance, engrossment,
   equability, equanimity, equilibrium, eternalness, eternity,
   evenness, ever-duringness, everlastingness, everness,
   faithworthiness, featurelessness, fidelity, firmness, fixedness,
   foreverness, frozenness, fullness, gaplessness, gentleness,
   golden mean, happy medium, hardening, hardness, homogeneity,
   immobility, immovability, immovableness, immutability,
   impartiality, incessancy, indefatigability, indestructibility,
   industriousness, industry, infinite duration, infinity, insistence,
   insistency, interminability, invariability, invariableness,
   inveteracy, invincibility, jointlessness, judiciousness,
   juste-milieu, lastingness, lenity, long standing, long-lastingness,
   long-livedness, longevity, loyalty, maintenance, mass, materiality,
   meden agan, middle way, mildness, moderateness, moderation,
   moderationism, monolithism, monotony, neutrality, never-endingness,
   nonviolence, nothing in excess, obstinacy, pacifism, palpability,
   patience, patience of Job, perdurability, perennation,
   perenniality, perennialness, permanence, permanency, perpetualness,
   perpetuity, perseverance, persistence, persistency,
   pertinaciousness, pertinacity, plenitude, plodding, plugging,
   ponderability, predictability, preoccupation, prudence, quiescence,
   relentlessness, reliability, repose, resoluteness, resolution,
   resolve, restraint, rigidity, seamlessness, secureness, security,
   sedulity, sedulousness, self-abnegation, self-control, self-denial,
   self-restraint, sempiternity, serenity, single-mindedness,
   singleness of purpose, slogging, smoothness, sobriety, solidity,
   solidness, soundness, stableness, stamina, standing, stasis,
   staunchness, staying power, steadfastness, steadiness,
   steady state, stick-to-itiveness, stoutness, strength,
   stubbornness, sturdiness, substance, substantiality,
   substantialness, successiveness, survival, survivance, tangibility,
   temper, temperance, temperateness, tenaciousness, tenacity,
   timelessness, tirelessness, torpor, toughness, tranquillity,
   trustworthiness, unbrokenness, unceasingness, unchangeability,
   unchangingness, undifferentiation, unerringness, unexcessiveness,
   unextravagance, unextremeness, uniformity, unintermittedness,
   uninterruptedness, uninterruption, unity, unrelievedness,
   unremittingness, unruffledness, unswerving attention, validity,
   via media