Picketer rhymes with:
benscoter, marketer, secateur, accelerometer, altimeter, altvater, amphitheater, amphitheatre, anemometer, benatar, benscoter, capacitor, catheter, comparator, competitor, conservator, conspirator, contributor, creditor, densitometer, diameter, distributor, dynamometer, editor, elater, eletr, estimator, executor, exhibitor, fluorometer, goniometer, hochstatter, hovater, hovatter, hydrometer, hygrometer, inheritor, inhibitor, inquisitor, interferometer, interlocutor, interpreter, janitor, jupiter, kilometer, magnetometer, marketer, meritor, micrometer, monitor, odometer, orator, orbiter, parameter, perimeter, polarimeter, predator, proprietor, quieter, rioter, secateur, senator, solicitor, spectrometer, speedometer, stiefvater, streitmatter, strittmatter, theater, theatre, thermometer, trumpeter, visitor, wiater
Picketer sounds like:
pacesetter, pachter, paster, pasteur, pastor, pastora, pastore, pastry, pasture, pasztor, peachtree, pesatori, pescatore, pester, pfiester, pfiesteria, pfister, pfisterer, picture, pistor, pistorio, poster, posteraro, posterior, posture, postwar, psychiatry, pusateri