hey,

Use Drived Column Component before Data conversion and use this expression

TRIM(birth_date) == "" ? (DT_DBTIMESTAMP)NULL(DT_DBTIMESTAMP) : (DT_DBTIMESTAMP)(DT_STR,10,1252)(SUBSTRING(TRIM(birth_date),5,4) + "/" + SUBSTRING(TRIM(birth_date),1,2) + "/" + SUBSTRING(TRIM(birth_date),3,2))

it will replace the empty string by nulll.

it will work..