The Collaborative International Dictionary of English v.0.48:

Complaisant \Com"plai*sant\, a. [F. complaisant, p. pr. of
   complaire to acquiesce as a favor, fr. L. complacere. See
   Complacent.]
   Desirous to please; courteous; obliging; compliant; as, a
   complaisant gentleman.
   [1913 Webster]

         There are to whom my satire seems too bold:
         Scarce to wise Peter complaisant enough. --Pope.

   Syn: Obliging; courteous; affable; gracious; civil; polite;
        well-bred. See Obliging. -- Com"plai*sant`ly, adv.
        -- Com"plai*sant`ness, n.
        [1913 Webster]