The Collaborative International Dictionary of English v.0.48:

Punster \Pun"ster\, n.
   One who puns, or is skilled in, or given to, punning; a
   quibbler; a low wit.
   [1913 Webster]

WordNet (r) 3.0 (2006):

punster
    n 1: someone overly fond of making puns

Moby Thesaurus II by Grady Ward, 1.0:

32 Moby Thesaurus words for "punster":
   banana, burlesquer, caricaturist, clown, comedian, comic, cutup,
   epigrammatist, funnyman, gag writer, gagman, gagster, humorist,
   ironist, jester, joker, jokesmith, jokester, lampooner, madcap,
   parodist, prankster, punner, quipster, reparteeist, satirist, wag,
   wagwit, wisecracker, wit, witling, zany