Argentine rhymes with:
constantine, florentine, quarantine, constantine, elephantine, florentine, konstantin, quarantine, albertine, aronstein, augustine, bartlestein, boeschenstein, braunstein, brillstein, bronstein, buckstein, carotene, constantine, dobberstein, eckstein, egbertine, elbertine, elephantine, epstein, ernestine, feuerstein, fierstein, finkelstein, florentine, fromstein, glickstein, goberstein, grinstein, grubstein, grudenstein, guillotine, hammerstein, heseltine, holstein, konstantin, libertine, lichtenstein, lipstein, mangosteen, muscatine, nicotine, nothstein, osteen, pfundstein, philistine, protein, quarantine, rubinstein, safferstein, schottenstein, silberstein, silverstein, springsteen, vogelstein, wasserstein, wetstein, wintersteen, zumstein
Argentine sounds like:
aircondition, argentina, argentinian, argumentation