Legal provisions for optional referendums at national level
Barbados
Answer
No, but ad hoc referendums are possible
Source
Constitution 2002
http://aceproject.org/ero-en/regions/americas/BB/barbados-the-constitution-of-barbados-2012
The Representation of the People Act (2007)
http://aceproject.org/ero-en/regions/americas/BB/barbados-representation-of-the-people-act-2007
Referendum Act, 2005
http://aceproject.org/ero-en/regions/americas/BB/barbados-referendum-act-2005-2012
Comment
No standing legislation addressing direct democracy in the legislation of the country. There is a legislation for one particular referendum that was meant to be held but which never actually took place:
