The Netherlands embassy in Riga does not issue visa.
Latvia is part of the Schengen area. Do you have the nationality of Latvia? Or do you have a valid Schengen visa or a residence permit for Latvia? 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.