So you're using the mod_customcert plugin? Which version? And which Moodle version?
Do you want arbitrary issued dates? One can have an arbitrary date across all certificates by replacing the date field with a text field containing the required date. But this won't work if you wanted arbitrary dates for individual certificates.
The date field needs a "date item" which is its data source, for example, issued date (the date the certificate was awarded), an activity's completion date, or the course completion date. You could alter these dates in the database. However this will also alter the corresponding date, for example, if you changed an activity completion date for a student to change what's shown on the certificate this date would also be changed in the activity completion report. If you're considering modifying the database be very, very careful and make sure you perform a database backup first.
It might help us to suggest ideas if you explained more about the motivation for your requirement.