If you are using a store procedure inserting data into the table, you don't really need a trigger. You first check if the combination exists then don't insert.
CREATE PROCEDURE usp_InsertData
@Name varchar(50),
@Date DateTime
AS
BEGIN
IF (SELECT COUNT(*) FROM tblData WHERE Name = @Name AND Date=@Date) = 0
BEGIN
INSERT INTO tblData
( Name, Date)
VALUES (@Name, @Date)
Print 'Data now added.'
END
ELSE
BEGIN
Print 'Dah! already exists';
END
END
The below trigger can used if you are not inserting data via the store procedure.
CREATE TRIGGER checkDuplicate ON tblData
AFTER INSERT
AS
IF EXISTS ( SELECT * FROM tblData A
INNER JOIN inserted B ON B.name=A.name and A.Date=B.Date)
BEGIN
RAISERROR ('Dah! already exists', 16, 1);
END
GO