REPLACE empty string

You can use CASE for this.

(CASE WHEN *YOURTHING* = '' THEN '0' ELSE *YOURTHING* END) 
AS *YOURTHING*

There is nothing to replace in an empty string. REPLACE replaces a sequence of characters in a string with another set of characters.

You could use NULLIF to treat it as NULL + COALESCE (or ISNULL):

declare @value varchar(10);
set @value = '';
SELECT COALESCE(NULLIF(@value,''), '0')

This returns '0'.