Theiler rhymes with:
beiler, bleiler, blyler, byler, compiler, cuyler, eiler, feiler, filer, geiler, heiler, hiler, huyler, hyler, iler, isler, kyler, miler, myler, pilar, pliler, plyler, schuyler, seiler, siler, syler, tyler, weiler, wiler, wyler, zeiler
Theiler sounds like:
tailor, taller, tattler, tayler, taylor, teetotaler, teller, tellier, thaler, tiller, tillery, titular, toddler, tolar, toler, toller, towler, tullar, tuller, tullier, tutwiler, tyler