The Collaborative International Dictionary of English v.0.48:

Customarily \Cus"tom*a*ri*ly\ (-[asl]*r[i^]*l[y^]), adv.
   In a customary manner; habitually.
   [1913 Webster]

WordNet (r) 3.0 (2006):

customarily
    adv 1: by custom; according to common practice; "children are
           custosby-the-waymarily expected to be seen but not heard"

Moby Thesaurus II by Grady Ward, 1.0:

33 Moby Thesaurus words for "customarily":
   according to use, accustomedly, as a rule, as is proper,
   as is usual, as per usual, as things go, as usual, chiefly,
   comme il faut, commonly, consistently, conventionally, correctly,
   decorously, generally, habitually, mainly, most often, mostly,
   naturally, normally, normatively, ordinarily, orthodoxly,
   prescriptively, properly, regularly, routinely, to be expected,
   traditionally, usually, wontedly