Exigency rhymes with:
agency, cogency, contingency, counterinsurgency, emergency, insurgency, interagency, nonemergency, regency, resurgency, stringency, urgency
Exigency sounds like:
eakins, easing, easygoing, echinacea, echoing, economic, economico, economics, economies, economize, economizes, economos, economy's, egging, eggnog, eggnogs, egomaniac, eischens, eisenach, eking, ekins, equinox, escamez, eschewing, eskenazi, eskimos, essence, eugenia's, eugenic, eugenics, eugenio's, examines, examining, exams, exchange, exchange's, exchanges, exchanges', excusing, exhumes, exigencies, exim's, exogenous, exxon's