You want something like this:
CREATE FUNCTION Convert_Date(@Cdate DATE)
RETURNS DATE
AS
BEGIN
DECLARE @return DATE
SELECT @return =
(
CASE LEFT(@Cdate,1)
WHEN '1' THEN CONVERT(DATE, ('19'+ CONVERT(VARCHAR(30), RIGHT(@Cdate,6))))
WHEN '2' THEN CONVERT(DATE, ('20'+ CONVERT(VARCHAR(30), RIGHT(@Cdate,6))))
END
)
RETURN @return
END
Your when statements should be the times when your result matches the case.