Vigorous rhymes with:
rigorous, rigorous, adulterous, adventurous, amorous, avarice, barbarous, boisterous, cancerous, cantankerous, carboniferous, carnivorous, coniferous, dangerous, decorous, fossiliferous, generous, glamorous, hatteras, herbivorous, heterosporous, homosporous, humerous, humerus, humorous, insectivorous, lazarus, lecherous, murderous, numerous, obstreperous, odorous, omnivorous, onerous, overgenerous, oviparous, ovoviviparous, phosphorous, phosphorus, ponderous, precancerous, preposterous, prosperous, rancorous, rapturous, rhinoceros, rigorous, slanderous, sonorous, temerous, tetramerous, thunderous, timorous, traitorous, treacherous, unglamorous, uterus, viviparous, vociferous
Vigorous sounds like:
vagaries, vicarious, vicars, vickers, visors, voicework, voiceworks, vouchers, voyager's, voyagers