Allegedly rhymes with:
acidly, advisedly, assuredly, avidly, avowedly, belatedly, blessedly, contentedly, decidedly, deservedly, determinedly, doggedly, excitedly, intrepidly, markedly, morbidly, rapidly, reportedly, ruggedly, solidly, splendidly, stupidly, supposedly, timidly, unashamedly, vividly