The Collaborative International Dictionary of English v.0.48:

Peevish \Pee"vish\, a. [OE. pevische; of uncertain origin, perh.
   from a word imitative of the noise made by fretful children +
   -ish.]
   1. Habitually fretful; easily vexed or fretted; hard to
      please; apt to complain; querulous; petulant. "Her peevish
      babe." --Wordsworth.
      [1913 Webster]

            She is peevish, sullen, froward.      --Shak.
      [1913 Webster]

   2. Expressing fretfulness and discontent, or unjustifiable
      dissatisfaction; as, a peevish answer.
      [1913 Webster]

   3. Silly; childish; trifling. [Obs.]
      [1913 Webster]

            To send such peevish tokens to a king. --Shak.
      [1913 Webster]

   Syn: Querulous; petulant; cross; ill-tempered; testy;
        captious; discontented. See Fretful.
        [1913 Webster]

WordNet (r) 3.0 (2006):

peevish
    adj 1: easily irritated or annoyed; "an incorrigibly fractious
           young man"; "not the least nettlesome of his countrymen"
           [syn: cranky, fractious, irritable, nettlesome,
           peevish, peckish, pettish, petulant, scratchy,
           testy, tetchy, techy]

Moby Thesaurus II by Grady Ward, 1.0:

92 Moby Thesaurus words for "peevish":
   Jeremianic, acrimonious, bad-tempered, beefing, bellyaching,
   bilious, bitching, cantankerous, captious, carping, catty,
   caviling, cavilling, churlish, complaining, complaintful, crabbed,
   crabbing, crabby, cranky, critical, croaking, cross, crotchety,
   crusty, disappointed, discontented, disgruntled, displeased,
   dissatisfied, envious, faultfinding, fractious, fretful, griping,
   grouchy, grousing, growling, grumbling, grumpish, grumpy, howling,
   huffy, ill-humored, ill-natured, ill-tempered, irritable,
   lamentive, malcontent, malcontented, moanful, mournful, murmuring,
   muttering, nagging, naggy, out of humor, pettish, petulant,
   plaintive, plangent, puling, querulant, querulous, rebellious,
   resentful, restive, restless, short-tempered, shrewish, snappish,
   sorrowful, splenetic, sulky, testy, tetchy, touchy, ululant,
   unaccepting, unaccommodating, uneasy, unfulfilled, ungratified,
   unhappy, unsatisfied, vixenish, vixenly, wailful, waspish,
   whimpering, whining, whiny