You probably can get the desired result by means of a simple trigger, assuming your version of MySQL supports those. Consider the table:
id ephem value1 value2
1 1412 this that
2 2317 the other
(&c.)
In this example, ephem
is the number of seconds since midnight at the time the row was created, which obviously will reset to zero at midnight every day. You can automatically set this value at row creation time using the following trigger, which worked as intended on the MySQL 5.1.66 instance where I tested it:
CREATE TRIGGER set_ephemeral_day_value
BEFORE INSERT ON table
FOR EACH ROW
SET new.ephem = CAST(MOD(UNIX_TIMESTAMP(), 86400) AS UNSIGNED INTEGER);