Competent rhymes with:
penitent, ahrendt, ament, arendt, argent, bedient, behrendt, berendt, dissident, encampment, figment, forint, gunflint, ifint, lucent, milicent, millicent, myoscint, penitent, pertinent, preadolescent, prudente, skinflint, succulent, techint, tumescent, varmint
Competent sounds like:
combatant, confidant, confidante, confident