Invariant rhymes with:
variant, variant, miscreant, nutrient, prurient, variant, affiant, ambient, cordiant, defoliant, deviant, disobedient, expedient, gradient, incipient, ingredient, lenient, luxuriant, miscreant, nutrient, obedient, percipient, prescient, prurient, radiant, recipient, salient, subservient, variant
Invariant sounds like:
impairment, imprint, imprinted, infirmed, infirmity, informant, informed