Are you looking for records created between '2-23-04 10:00 pm' and '2-28-04 02:00 am' ?
If so try this ...
Select z.State,d.Affiliate,count(*)
From Call_Center_Data c ,Zip_PZA z, DNIS d
where c.zip_code = z.zip_code
and c.dnis_code = d.dnis
and c.Response_Date between '2-23-04 22:00:00' and '2-28-04 02:00:00'
group by z.state,d.Affiliate

OR
Are you looking for records created between '10:00 pm' and '02:00 am' everyday during '2-23-04' to '2-28-04' ?
If so try this ...

try this..
Select z.State,d.Affiliate,count(*)
From Call_Center_Data c ,Zip_PZA z, DNIS d
where c.zip_code = z.zip_code
and c.dnis_code = d.dnis
and c.Response_Date between '2-23-04' and '2-28-04'
and (CONVERT(char(12), c.Response_Date,8) between '22:00:00' and '23:59:00'
or CONVERT(char(12), c.Response_Date,8) between '00:00:00' and '02:00:00'
)
group by z.state,d.Affiliate