The Collaborative International Dictionary of English v.0.48:

Importunate \Im*por"tu*nate\ ([i^]m*p[^o]r"t[-u]*n[asl]t), a.
   [See Importune.]
   1. Troublesomely urgent; unreasonably solicitous;
      overpressing in request or demand; urgent; teasing; as, an
      importunate petitioner, curiosity. --Whewell.
      [1913 Webster]

   2. Hard to be borne; unendurable. [R.] --Donne. --
      Im*por"tu*nate*ly, adv. -- Im*por"tu*nate*ness, n.
      [1913 Webster]

WordNet (r) 3.0 (2006):

importunate
    adj 1: expressing earnest entreaty; "an importunate job
           applicant"

Moby Thesaurus II by Grady Ward, 1.0:

75 Moby Thesaurus words for "importunate":
   aggravating, annoying, bothering, bothersome, cajoling, choiceless,
   clamant, clamorous, coaxing, compulsory, controlled, crying,
   demanding, disturbing, draining, dunning, exacting, exasperating,
   exigent, exorbitant, extortionate, firm-minded, forward, galling,
   grasping, harassing, imperative, importune, independent, insistent,
   instant, irking, irksome, irritating, loud, mandatory, nagging,
   necessary, necessitous, obligatory, persistent, pertinacious,
   pesky, pestering, pestiferous, pestilent, pestilential, plaguesome,
   plaguey, plaguing, pressing, provoking, pushy, self-asserting,
   self-assertive, self-controlled, self-expressive, self-possessed,
   self-restrained, strong-minded, strong-willed, taxing, teasing,
   tiresome, tormenting, troublesome, troubling, urgent, vexatious,
   vexing, wearisome, wheedling, without choice, worrisome,
   worrying