Postdates rhymes with:
date's, dates, predates, sedates, updates, abates, annotates, ates, awaits, aytes, baits, bates, bates', cates, coates, conflates, conjugates, crates, creates, date's, dates, debate's, debates, delegates', demodulates, desecrates, dictates, eight's, eights, elates, equates, estate's, estates, fates, frates, gates, gates', grates, great's, greats, hates, inflates, interstate's, kate's, kates, kuwait's, lecates, mates, misstates, narrates, negates, overrates, pates, plaits, plates, predates, procreates, rate's, rates, relates, restates, sates, scates, sedates, skates, slates, spates, speights, state's, states, states', straights, straits, tate's, traits, translates, updates, waite's, waites, waits, weights, yates, yeats, zaitz
Postdates sounds like:
packets, packwood's, pact's, pacts, pagoda's, pagodas, pas-de-deux, pastas, pastes, pastiche, pastiches, pasts, pectic, pesetas, pestka, pests, phagocytes, physicists, piaget's, pickets, pickett's, picts, pistachio, pistachios, pockets, posits, post's, post-attack, postage, posts, psychotic, pussycats