Scandinavian Airlines has round-trip flights from Newark/New York (EWR) to Copenhagen (CPH) for $382-$401, NONSTOP. Flights September, October, November, January, February, and March. Extended weekends available.
Carry on bag with a maximum weight of 18 lbs is allowed for free on SAS. You can avoid seat selection fees by accepting the randomly assigned seat at the gate. Upgrading to a higher fare class that includes a full-size carry-on bag for $28 may be cheaper than booking the discount fare with the added carry-on bag fee (for about $60).