Well, you can include the parent_id condition with:
:conditions => ["created_at = ? and parent_id is null", @date]
But your date stuff worries me. created_at is a timestamp, so you'll never get a match (unless the time on the timestamp is 00:00:00). If you want all the timestamps for a date, you need to find timestamps in a 24-hour range, right?
Something like:
:conditions => ["created_at between ? and ? and parent_id is null", Date.today, Date.today+1]