As the others have sad, index is the best choice for performance reasons.
In case you have to go the trigger route, a variation of the trigger stmt: ( sorry, didn't test it)
Code:
CREATE TRIGGER NyTrig NO CASCADE BEFORE INSERT ON MyTable
REFERENCING NEW as newdata FOR EACH ROW MODE DB2SQL
WHEN EXISTS (select 1 from MyTable as mt where (mt.col1 = newdata.col1 and mt.col2 = newdata.col2) )
SIGNAL SQLSTATE '75001' set message_text = ' There cannot be two entries on the same day'