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]

WordNet (r) 3.0 (2006):

complaisant
    adj 1: showing a cheerful willingness to do favors for others;
           "to close one's eyes like a complaisant husband whose
           wife has taken a lover"; "the obliging waiter was in no
           hurry for us to leave" [syn: complaisant, obliging]

Moby Thesaurus II by Grady Ward, 1.0:

121 Moby Thesaurus words for "complaisant":
   abject, accepting, accommodating, accommodative, acquiescent,
   adaptable, adaptive, adjustable, affable, agreeable, amiable,
   amicable, assenting, attentive, benevolent, benign, benignant,
   blissful, cheerful, civil, compatible, compliable, compliant,
   complying, conformable, congenial, consenting, considerate,
   cordial, courteous, decent, deferential, delicate, desirable,
   dulcet, easy, en rapport, enjoyable, fair, fair and pleasant,
   felicific, felicitous, fine, flexible, generous, genial, gentle,
   good, good-humored, good-natured, good-tempered, goodly, graceful,
   gracious, grateful, gratifying, harmonious, heart-warming, heedful,
   helpful, honeyed, indulgent, kind, kindly, lenient, likable,
   malleable, mellifluous, mellow, mellowy, mild, mindful,
   mindful of others, mollified, nice, nondissenting, nonresistant,
   nonresisting, nonresistive, nonrigid, obedient, obliging,
   other-directed, overindulgent, overpermissive, passive, permissive,
   plastic, pleasant, pleasing, pleasurable, pleasure-giving,
   pleasureful, pliant, polite, regardful, resigned, respectful,
   rewarding, satisfying, servile, soft, soft as putty, softened,
   solicitous, submissive, subservient, supine, sweet, tactful,
   tender, thoughtful, tolerant, tractable, unassertive,
   uncomplaining, unresistant, unresisting, urbane, welcome,
   whisper-soft