The Collaborative International Dictionary of English v.0.48:

Affirmant \Af*firm"ant\ ([a^]f*f[~e]rm"ant), n. [L. affirmans,
   -antis, p. pr. See Affirm.]
   1. One who affirms or asserts.
      [1913 Webster]

   2. (Law) One who affirms, instead of taking an oath.
      [1913 Webster]

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

AFFIRMANT, practice. One who makes affirmation instead of making oath that
the evidence which he is about to give shall be the truth, as if he had been
sworn. He is liable to all the pains and penalty of perjury, if he shall be
guilty of willfully and maliciously violating his affirmation.