Cynically rhymes with:
clinically, chronically, clinically, electronically, sardonically, technically, chronically, clinically, comically, critically, diametrically, electrically, electronically, empirically, ethically, fanatically, geographically, hermetically, historically, intrinsically, journalistically, magically, magnetically, majestically, mathematically, methodically, metrically, mineralogically, optimistically, parenthetically, pathetically, periodically, philosophically, physically, politically, pragmatically, ritualistically, romantically, sardonically, scientifically, skeptically, statistically, surgically, symbolically, sympathetically, tactically, technically, technologically, theatrically, theoretically, therapeutically, uncritically
Cynically sounds like:
cancel, canchola, cancilla, caniglia, canonical, cencall, chemical, chemically, chinchilla, cianciola, cianciolo, cianciulli, cimaglia, comical, comically, commingle, conceal, concisely, congeal, conical, coniglio, conjugal, conjul, conkel, conkle, consciously, consiglio, consol, console, consoli, consolo, consuela, consul, council, counsel, counsell, cynical