Patagonian rhymes with:
oregonian, gorgonian, oregonian, amazonian, andonian, apollonian, babylonian, bostonian, caledonian, devonian, draconian, estonian, gorgonian, houstonian, jacksonian, jeffersonian, melkonian, newtonian, oregonian, plutonian, simonian, smithsonian, usoniam, washingtonian
Patagonian sounds like:
patagonia, patchen, patchin, pathogen, patteson, pattison, petitjean, pettijohn, pidgeon, pietism, pitchman, pitchmen, pitkin, pitswon, pitzen, potassium