How can I create a SQL unique constraint based on 2 columns?

You can try this:

CREATE UNIQUE CLUSTERED INDEX index_name ON TABLE (col1,col2)

or

CREATE UNIQUE NONCLUSTERED INDEX index_name ON TABLE (col1,col2)

or

ALTER TABLE [dbo].[TABLE] ADD CONSTRAINT
    UNIQUE_Table UNIQUE CLUSTERED
    (
       col1,
       col2
    ) ON [PRIMARY]