Dictionary: rhymer   (rī'mər)

One who composes rhymes.

noun

One who writes poetry: bard, muse², poet, poetaster, poetess, rhymester, versifier. See words.

n.

A poet regarded with indifference or disesteem.

    The rimer quenches his unheeded fires,
    The sound surceases and the sense expires.
    Then the domestic dog, to east and west,
    Expounds the passions burning in his breast.
    The rising moon o'er that enchanted land
    Pauses to hear and yearns to understand.
                                                         Mowbray Myles

The noun has one meaning:

Meaning #1: a writer who composes rhymes; a maker of poor verses (usually used as terms of contempt for minor or inferior poets)
  Synonyms: rhymester, versifier, poetizer, poetiser