Try adding the correct style parameter to your convert function (see MSDN: link )
ie CONVERT(DATETIME, NewsDate, 111)
(111 is the style for YYYY/MM/DD)
Then you get:
SELECT *
FROM News_Table
WHERE (DATEDIFF( DAY ,
CONVERT(DATETIME, NewsDate, 111) ,
CONVERT(DATETIME,@Todaydate, 111)
) <= @Count)