ALTER TABLE `downloads` ADD `date` DATETIME NOT NULL DEFAULT CURRENT_TIMESTAMP ;

ALTER TABLE `downloads` ADD `date` TIMESTAMP NOT NULL DEFAULT CURRENT_TIMESTAMP ;

ALTER TABLE `downloads` ADD `date` DATETIME NULL; -- date must allow
                                                  -- NULLs or default
                                                  -- to a special value
DROP TRIGGER IF EXISTS downloads_BI;
DELIMITER //
CREATE TRIGGER downloads_BI
BEFORE INSERT ON downloads FOR EACH ROW
BEGIN
    IF (NEW.date IS NULL) THEN -- change the isnull check for the default used
        SET NEW.date = now();
    END IF;
END//
DELIMITER ;

mysql> INSERT INTO downloads (i) VALUES (1); -- I do not set date
Query OK, 1 row affected (0.00 sec)

mysql> SELECT * FROM downloads;
+------+---------------------+
| i    | date                |
+------+---------------------+
|    1 | 2016-03-22 09:27:52 |
+------+---------------------+
1 row in set (0.00 sec)