Puppetry rhymes with:
altimetry, asymmetry, banditry, basketry, bigotry, cabinetry, circuitry, dissymmetry, gadgetry, geometry, helotry, idolatry, optometry, poetry, psychiatry, punditry, rocketry, spectrometry, symmetry, telemetry, toiletry, zealotry
Puppetry sounds like:
padre, padro, pater, patera, patrie, patry, patter, pedro, peter, petery, petr, petra, petre, petrea, petree, petrey, petri, petrie, petro, petrow, petru, petry, petter, pettry, pewter, phedra, piedra, pieter, pietro, piotter, pipetter, pitre, pituitary, poetry, poitier, poitra, pothier, potier, potter, pottery, poudrier, pouter, poutre, powder, powdery, powter, puder, puppeteer, putter, putterer