The Collaborative International Dictionary of English v.0.48:

Sleepiness \Sleep"i*ness\, n.
   The quality or state of being sleepy.
   [1913 Webster]

WordNet (r) 3.0 (2006):

sleepiness
    n 1: a very sleepy state; "sleepiness causes many driving
         accidents" [syn: sleepiness, drowsiness, somnolence]
         [ant: sleeplessness, wakefulness]

Moby Thesaurus II by Grady Ward, 1.0:

59 Moby Thesaurus words for "sleepiness":
   acedia, apathy, boredom, brain fag, debilitation, debility,
   drowsiness, dullness, enervation, enfeeblement, ennui, eyestrain,
   faintness, fatigue, goneness, heart strain, heaviness, hebetude,
   inanimation, indifference, jadedness, lackadaisicalness,
   languidness, languishment, languor, languorousness, lassitude,
   lenitude, lentor, lethargy, lifelessness, listlessness,
   mental fatigue, mental strain, oscitancy, overstrain,
   overtiredness, passivity, phlegm, satedness, sloth, slothfulness,
   slowness, sluggishness, somnolence, stance fatigue, strain,
   stupefaction, stupor, supineness, tiredness, torpidity, torpidness,
   torpitude, torpor, weakness, wearifulness, weariness,
   world-weariness