Perseveres rhymes with:
reveres, veers, viers, adheres, algiers, amir's, appears, arrears, auctioneers, bandoliers, bassir's, beers, beers', bombardiers, budgeteers, careers, cashier's, cashiers, cavaliers, cheers, clears, coheres, conventioneers, debeers, deere's, disappears, ears, electioneers, engineers, engineers', fears, financiers, frontier's, frontiers, gear's, gears, gondoliers, guinier's, here's, interferes, marketeers, mears, miears, mir's, mutineers, nears, pamphleteers, peers, piers, pioneer's, pioneers, premier's, premieres, premiers, profiteers, queers, racketeers, reappears, rears, reveres, schweers, sears, sears', shamir's, smears, sneers, souvenirs, spears, speirs, spheres, steers, summiteers, sweers, tangiers, veers, veneers, viers, volunteers, wagoneers, wazir's, year's, years, years', zaire's
Perseveres sounds like:
prisburg, prosperous, prospers