Right now, January/2020 and February/2020 are the cheapest months to travel to Copenhagen. You will pay the most in April/2020.
SAS fly direct to Copenhagen from the United States of America.
The cheapest airline to fly from the United States of America to Copenhagen is Icelandair.
The best airline to fly between the United States of America and Copenhagen is Lufthansa. If you need direct flights then SAS is best.