Neither rhymes with:
breather, either, altogether, another, atither, bather, bellwether, birdfeather, bither, blather, bother, breather, brother, cather, crowther, dither, either, fairbrother, fairweather, farther, father, feather, forefather, further, futher, gather, genther, get-together, ginther, godfather, godmother, grandfather, grandmother, grether, guinther, heather, hesther, hither, huether, koether, kuether, lather, lawther, leather, lowther, mather, mayweather, meriweather, meriwether, merriweather, merriwether, mother, nether, norther, nother, oldfather, other, prather, raether, rather, reither, reuther, roether, ryther, sather, seither, sether, slather, slither, smather, smither, smoother, smother, souther, starkweather, stepfather, stepmother, stikeleather, strother, suther, tether, together, weather, werther, whether, whither, wither, wrather, yother, zither
Neither sounds like:
n'dour, nader, nadir, natter, nature, neater, neathery, nedrow, needier, neider, nether, nethery, netter, netware, neuter, nieder, niederer, nitro, notaro, notary, noteware, nother, notre, notter, nutri, nutria, nutter