SELECT FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01')));

実行結果

mysql> SELECT FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01')));
+----------------------------------------------------------------------------------------------------------------------+
| FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01'))) |
+----------------------------------------------------------------------------------------------------------------------+
| 2017-02-05 08:20:52.189146                                                                                           |
+----------------------------------------------------------------------------------------------------------------------+
1 row in set (0.00 sec)

mysql> SELECT FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01')));
+----------------------------------------------------------------------------------------------------------------------+
| FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01'))) |
+----------------------------------------------------------------------------------------------------------------------+
| 2017-02-02 23:37:49.727271                                                                                           |
+----------------------------------------------------------------------------------------------------------------------+
1 row in set (0.00 sec)

mysql> SELECT FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01')));
+----------------------------------------------------------------------------------------------------------------------+
| FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01'))) |
+----------------------------------------------------------------------------------------------------------------------+
| 2017-02-04 21:06:32.087503                                                                                           |
+----------------------------------------------------------------------------------------------------------------------+
1 row in set (0.00 sec)

mysql> SELECT FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01')));
+----------------------------------------------------------------------------------------------------------------------+
| FROM_UNIXTIME(UNIX_TIMESTAMP('2017-02-01') + RAND() * (UNIX_TIMESTAMP('2017-02-08') - UNIX_TIMESTAMP('2017-02-01'))) |
+----------------------------------------------------------------------------------------------------------------------+
| 2017-02-07 10:39:11.274294                                                                                           |
+----------------------------------------------------------------------------------------------------------------------+
1 row in set (0.00 sec)