Patagonia rhymes with:
gonia, adonia, amazonia, ansonia, antonia, caledonia, colonia, cydonia, diaphonia, donia, estonia, gastonia, gonia, harmonia, idonia, latonia, macedonia, madonia, new-caledonia, omonia, petronia, philharmonia, rondonia, sidonia, sinfonia, slavonia, slovonia, sophronia, tonia, vernonia, vidonia
Patagonia sounds like:
patagonian, patchen, patchin, pathogen, patteson, pattison, petitjean, pettijohn, pidgeon, pietism, pitchman, pitchmen, pitkin, pitswon, pitzen, potassium