The Netherlands embassy in Copenhagen does not issue visa.
Denmark is part of the Schengen area. Do you have the nationality of Denmark? Or do you have a valid Schengen visa or a residence permit for Denmark? Then you do not need to apply for a long-stay Caribbean visa to travel to the Caribbean part of the Netherlands (Aruba, Bonaire, Curaçao, Saba, St Eustatius or St Maarten).
If you want to stay in the Caribbean parts of the Kingdom for longer than 90 days, you will normally need a residence permit.
In case you do need a long-stay Caribbean visa, please send an e-mail to the Netherlands embassy in Copenhagen with your full name, contact details and your situation. The embassy will inform you about the possibilities.