If you are going with the standard "2, 4, 6, 8..." chant, here's a list of rhymes:
1 syllable:
ate, aydt, bait, bate, beit, cate, chait, crate, date, fait, fate, feight, fete, frate, freight, gait, gate, grate, great, haight, hait, hate, kate, late, leight, mate, nate, pait, pate, plate, rait, raitt, rate, sate, skate, slate, spate, speight, state, straight, strait, strate, streight, tait, taite, taitt, tate, trait, wait, waite, waitt, wayt, weight
2 syllables:
abate, and gate, au fait, await, bank rate, baud rate, bay state, belate, berate, birth rate, blind date, change state, charge plate, clean slate, coate, collate, conflate, create, crime rate, cut rate, debate, deflate, dictate, dilate, dose rate, duck pate, due date, elate, equate, est, estate, first mate, first state, flow rate, free state, freight rate, gem state, gold plate, gray skate, ground bait, growth rate, head gate, heart rate, home plate, hot plate, ice skate, inflate, innate, irate, iwate, kuwait, lightweight, lose weight, m-8, mccreight, mcfate, misstate, negate, not late, oblate, of late, ornate, or gate, pay rate, peach state, poor rate, postdate, predate, prorate, rain date, reflate, relate, restate, sash weight, sedate, slave state, sleep late, soul mate, soup plate, speed skate, stagflate, steel plate, sumgait, tail gate, tax rate, tin plate, to date, translate, tri-state, troy weight, update, upstate, wall plate
3 syllables:
armor plate, armour plate, badger state, balkan state, baltic state, bargain rate, beaver state, beehive state, bering strait, bluegrass state, body weight, buckeye state, buffer state, change of state, charles the great, chief of state, chinese date, city state, conjugate, cover plate, data rate, desecrate, dessert plate, diamond state, dinner plate, discount rate, disinflate, exchange rate, fashion plate, figure skate, finger plate, first estate, fourth estate, garden state, golden gate, golden state, gopher state, granite state, great lakes state, gross estate, hawkeye state, head of state, hoosier state, id est, interest rate, interstate, intrastate, keystone state, license plate, lie in wait, life estate, line of fate, little skate, mental state, mormon state, mountain state, multistate, net estate, new york state, north star state, nutmeg state, ocean state, old line state, old north state, overrate, overweight, payment rate, pine tree state, police state, prairie state, procreate, quarter plate, real estate, recreate, reinstate, rider plate, roller skate, running mate, sagebrush state, salad plate, sandwich plate, show me state, silverplate, silver plate, silver state, solid-state, sooner state, sparring mate, spin the plate, starting gate, sunshine state, tar heel state, telerate, third estate, thorny skate, threshold gate, treasure state, underrate, water gate, welfare state, wicket gate
4 syllables:
absentee rate, aloha state, atomic weight, attrition rate, at any rate, australian state, battle born state, cognitive state, collection plate, combining weight, coyote state, demodulate, ecstatic state, empire state, evergreen state, excursion rate, frederick the great, grand canyon state, green mountain state, herod the great, inflation rate, installment rate, interrelate, irish free state, junior lightweight, korean strait, korea strait, landed estate, louis the great, lying in wait, magnolia state, mount rushmore state, natural state, palmetto state, peace garden state, pelican state, pompey the great, prime interest rate, public debate, recriminate, remunerate, repayment rate, reporting weight, second estate, sunflower state, turnover rate, vacancy rate, volunteer state, wolverine state
5 syllables:
american state, atmospheric state, at an equal rate, catherine the great, centennial state, constitution state, department of state, emotional state, equality state, equivalent weight, exercising weight, fertility rate, gregory the great, maturity date, metabolic rate, mithridates the great, molecular weight, mortality rate, occupancy rate, old dominion state, personal estate, photographic plate, temporary state, unemployment rate
6 syllables:
a42128, alexander the great, capital of kuwait, depreciation rate, psychological state, secretary of state, sedimentation rate
7 syllables:
basal metabolic rate, infant mortality rate, physiological state
This came from an attempt to verbify emolument into emolumate
(OED says in ain't happenin')
Here's emolument from M-W online:
Etymology: Middle English, from Latin emolumentum advantage, from emolere to produce by grinding, from e- + molere to grind -- more at MEAL
1 : the returns arising from office or employment usually in the form of compensation or perquisites
