How can I make an automatic copy of a MySQL database to another MySQL database on the same server? I have two MySQL databases called LIVE and REPORTS on the same server.

I want to copy the LIVE database and all its contents into the REPORTS database everyday at a specific time frame between 1 am and 5 am.

How could I do this automatically?
You can setup second mysql instance with replication. If you need to "copy" only during certain time period, you may choose to cron a script which will start and stop replication according to the time.
Again you can only choose to replicate-do-db certain databases as well.