1 syllable:
-zyme, beim, brime, chime, chyme, climb, clime, crime, dime, drime, drms cime, glime, grime, haim, heim, hime, i'm, kime, knime, lime, lyme, mime, ni-mh, prhyme, prime, rhime, rhyme, s-mime, s/mime, seim, shime, shy'm, sime, slime, slyme, smime, spime, stime, syme, thym-, thyme, trime

2 syllables:
9x39mm, abzyme, airtime, all-time, alltime, arnheim, atime, azyme, bathtime, bedtime, begrime, belime, berhyme, berime, beslime, betime, big-time, bird-lime, birdlime, blenheim, blindheim, breaktime, brooklime, burnt lime, cat thyme, chatime, clothestime, coprime, crunchtime, daytime, delime, dislimb, dislimn, down-time, downtime, dreamstime, dreamtime, drive-time, drivetime, durkheim, e-crime, e-prime, enlimn, enzyme, escrime, estime, exptime, eye rhyme, facetime, first-time, flextime, floersheim, floresheim, florsheim, foretime, fragtime, full-time, fulltime, funtime, genzyme, good-time, half-time, halftime, head rhyme, hytime, infime, intime, joytime, kaihime, kaldheim, kamehime, kelheim, key lime, lead-time, life-time, lifetime, livetime, long-time, longtime, lunchtime, maytime, mealtime, meantime, mercyme, mistime, mordheim, mulheim, my-hime, naptime, nesheim, niflheim, night-time, nighttime, noontime, off-time, old-time, one-time, onetime, onfim, opheim, outclimb, part-time, parttime, passtime, pastime, peace-time, peacetime, peak-time, pforzheim, playtime, polheim, pre-crime, presstime, prime-time, primetime, quick-lime, quicklime, quicktime, ragtime, real-time, retime, rock-climb, run-time, runtime, ruptime, schooltime, screentime, seedtime, senhime, sensetime, septime, short-time, showtime, sinsheim, small-time, smalltime, solheim, sometime, sondheim, space-time, spacetime, springtime, stop-time, straszheim, sub-prime, sublime, subprime, sundheim, sweet lime, teatime, termtime, thoughtcrime, trondheim, true-crime, two-time, twotime, ultime, untime, upclimb, uptime, valheim, vice crime, waketime, waldheim, warehime, wartime, war crime, weinheim, werdesheim, why him?, wild thyme, windchime, windheim, wineheim, zonetime

3 syllables:
aforetime, aftertime, alextime, allozyme, amandime, anaheim, analcime, anticrime, anytime, archimime, basil thyme, beforetime, bettelheim, burgertime, buttenheim, caustic lime, christmastime, cinedigm, closing-time, co-enzyme, common thyme, countertime, creeping thyme, cybercrime, dinnertime, double-time, everytime, extra-time, flexitime, guggenheim, guggenheim's, hammertime, harvesttime, healthifyme, heppenheim, histozyme, hochenheim, hockenheim, hoffenheim, hyazyme, ingelheim, isocryme, isozyme, jotunheim, just-in-time, kissanime, kiyohime, kuenheim, lysozyme, mahanaim, mannerheim, maritime, mesenchyme, microzyme, monorhyme, movietime, muspelheim, nifelheim, oppenheim, oto-hime, otohime, overclimb, overtime, pac-in-time, pantomime, paradigm, parenchyme, pseudoprime, pulmazyme, pulmozyme, rapid climb, realtime, resublime, ribozyme, rochelime, rosenheim, schlagenheim, sclerenchyme, silver lime, soda lime, spanish lime, storytime, summertime, suppertime, tacotime, the sublime, tsukihime, undernime, undertime, vowel rhyme, wintertime, xenotime

4 syllables:
amazon prime, antienzyme, beginning rhyme, ceftazidime, cefuroxime, chloride of lime, consonant rhyme, erythrozyme, hydrated lime, initial rhyme, internal rhyme, in the meantime, japanese lime, michael morhaime, mise en abyme, mother-of-thyme, mother of thyme, multienzyme, nursery rhyme, organized crime, osakabehime, paroxetime, partner in crime, seine-maritime, superboy-prime, victimless crime

5 syllables:
7.62x39mm, almon-diblathaim, american lime, charente-maritime, ectomesenchyme, exponential-time, generalizedtime, jason oppenheim, multi-paradigm, once-in-a-lifetime, tamayori-hime, technetium-99m, toyotama-hime, wals-siezenheim

6 syllables:
newcastle-under-lyme, polynomial-time, programming paradigm, uwantme2killhim?, zodiac maritime

8 syllables:
konohanasakuya-hime