I would consider something like....
In your products table you will need a column to flag if the product is to be shown on the home page.
Then, create a PHP page that does the following:
1. Sets all the home page flags to 0
2. Has a recordset that randomly pulls back one product
3. Use Data Assist Update to set the home page flag to 1
You would then need to setup a Cron job on your server to run this script every day at Midnight.
Hope that helps?