The Collaborative International Dictionary of English v.0.48:

Rationally \Ra"tion*al*ly\, adv.
   In a rational manner.
   [1913 Webster]

WordNet (r) 3.0 (2006):

rationally
    adv 1: in a rational manner; "we must act rationally" [ant:
           irrationally]

Moby Thesaurus II by Grady Ward, 1.0:

32 Moby Thesaurus words for "rationally":
   analytically, artfully, astutely, circumspectly, cleverly,
   considerately, cunningly, discerningly, discreetly,
   in all conscience, in all reason, in reason, intelligently,
   judiciously, knowingly, logically, providently, prudently,
   reasonably, sagaciously, sanely, sensibly, shrewdly, smartly,
   soundly, syllogistically, thoughtfully, understandingly, wisely,
   within bounds, within reason, within reasonable limitations