The Collaborative International Dictionary of English v.0.48:

Pairing \Pair"ing\, n. [See Pair, v. i.]
   1. The act or process of uniting or arranging in pairs or
      couples.
      [1913 Webster]

   2. See To pair off, under Pair, v. i.
      [1913 Webster]

   Pairing time, the time when birds or other animals pair.
      [1913 Webster]