The Collaborative International Dictionary of English v.0.48:

Rhymer \Rhym"er\, n.
   One who makes rhymes; a versifier; -- generally in contempt;
   a poor poet; a poetaster.
   [1913 Webster]

         This would make them soon perceive what despicaple
         creatures our common rhymers and playwriters be.
                                                  --Milton.
   [1913 Webster]

WordNet (r) 3.0 (2006):

rhymer
    n 1: a writer who composes rhymes; a maker of poor verses
         (usually used as terms of contempt for minor or inferior
         poets) [syn: rhymer, rhymester, versifier,
         poetizer, poetiser]