shriner — a member of a fraternal order (Ancient Arabic Order of Nobles of the Mystic Shrine) that is an auxiliary of the Masonic order and is dedicated to good fellowship, health programs, charitable works, etc.
tyner — McCoy (Sulaimon Saud) born 1938, U.S. jazz pianist and composer.
whiner — to utter a low, usually nasal, complaining cry or sound, as from uneasiness, discontent, peevishness, etc.: The puppies were whining from hunger.
wiener — Norbert, 1894–1964, U.S. mathematician: pioneer in cybernetics.
refiner — to bring to a fine or a pure state; free from impurities: to refine metal, sugar, or petroleum.
reiner — Fritz, 1888–1963, Hungarian conductor in the U.S.
Four-or-more syllable rhymes
asia minor — large peninsula in W Asia, between the Black Sea and the Mediterranean, including Asiatic Turkey west of an undefined line from the Gulf of Iskenderun to the Black Sea
cargo liner — a cargo ship that sails regularly between designated ports according to a published schedule.
golden shiner — a small, silvery freshwater minnow, Notemigonus crysoleucas, native to eastern North America and introduced into western North America: often used as live bait in sport fishing.
ocean liner — an oceangoing passenger ship, operating either as one unit of a regular scheduled service or as a cruise ship.
party liner — a person who follows a party line, especially the Communist Party line.