The Collaborative International Dictionary of English v.0.48:

Importunity \Im`por*tu"ni*ty\, n.; pl. Importunities. [L.
   importunitas unsuitableness, rudeness: cf. F.
   importunit['e].]
   The quality of being importunate; pressing or pertinacious
   solicitation; urgent request; incessant or frequent
   application; troublesome pertinacity.
   [1913 Webster]

         O'ercome with importunity and tears.     --Milton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

importunity
    n 1: insistent solicitation and entreaty; "his importunity left
         me no alternative but to agree" [syn: importunity,
         urgency, urging]

Moby Thesaurus II by Grady Ward, 1.0:

25 Moby Thesaurus words for "importunity":
   blandishment, buttonholing, cajolement, cajolery, coaxing,
   demandingness, dunning, exigency, importunacy, importunateness,
   insistence, nagging, persistence, pertinaciousness, pertinacity,
   pestering, plaguing, plying, pressing, pressingness, pressure,
   teasing, urgency, urging, wheedling



Bouvier's Law Dictionary, Revised 6th Ed (1856):

IMPORTUNITY. Urgent solicitation, with troublesome frequency and
pertinacity.
     2. Wills and devises are sometimes set aside in consequence of the
importunity of those who have procured them. Whenever the importunity is
such as to deprive the devisor of the freedom, of his will, the devise
becomes fraudulent and void. Dane's Ab. ch. 127, a. 14, s. 5, 6, 7; 2
Phillim. R. 551, 2.