The Collaborative International Dictionary of English v.0.48:

Placidly \Plac"id*ly\, adv.
   In a placid manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

placidly
    adv 1: in a quiet and tranquil manner; "the sea now shimmered
           placidly before our eyes"
    2: in a placid and good-natured manner; "I put the questions,
       and she answered them placidly"

Moby Thesaurus II by Grady Ward, 1.0:

23 Moby Thesaurus words for "placidly":
   calmly, composedly, coolly, dispassionately, impassively,
   imperturbably, inexcitably, inirritably, levelheadedly, peacefully,
   quiescently, quietly, serenely, smoothly, steadily, still, stilly,
   stodgily, stoically, stolidly, stuffily, tranquilly,
   unperturbedly