Cox claimed the bronze medal in the series opener on the Toppa's Dream course, then backed up with silver in the second event.
Fellow NSWIS skier Nicole Parks was the other Australian woman in the medals, taking bronze in the second event.
Matt Graham was the best of the Aussie men, winning the qualifying round for the first event before skiing to silver in the final.
Rohan Chapman-Davies also flew the flag for the Aussie men, collecting bronze in the second round of the championships.
Japanese skiers dominated the men's, Sho Endo winning the first round with 23.75 points, ahead of Graham on 23.69.
His compatriot Nobuyuki Nishi won the second gold on offer, skiing to 24.27 points to oust US skier Reed Snyderman on 23.96. Chapman-Davies gained his bronze with 22.83 points.
US women took the two gold medals, Whitney Henceroth in the first round and Brittany Loweree in the second.