Changing a SUM returned NULL to zero

Put it outside:

SELECT COALESCE(

(  
    SELECT SUM(i.Logged)  
    FROM tbl_Sites s  
    INNER JOIN tbl_Incidents i  
    ON s.Location = i.Location  
    WHERE s.Sites = @SiteName AND i.[month] = DATEADD(mm, DATEDIFF(mm, 0, GetDate()) -1,0)  
    GROUP BY s.Sites  
), 0)  AS LoggedIncidents

If you are returning multiple rows, change INNER JOIN to LEFT JOIN

SELECT COALESCE(SUM(i.Logged),0)
FROM tbl_Sites s  
LEFT JOIN tbl_Incidents i  
ON s.Location = i.Location  
WHERE s.Sites = @SiteName AND i.[month] = DATEADD(mm, DATEDIFF(mm, 0, GetDate()) -1,0)  
GROUP BY s.Sites  

By the way, don’t put any function or expression inside aggregate functions if it’s not warranted, e.g. don’t put ISNULL, COALESCE inside of SUM, using function/expression inside aggregation cripples performance, the query will be executed with table scan