The Netherlands embassy in Budapest does not issue visa.
Hungary is part of the Schengen area. Do you have the nationality of Hungary? Or do you have a valid Schengen visa or a residence permit for Hungary? 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 make an appointment at the Netherlands embassy in Budapest.