Hmm, that might be a little more tricky as the SQL query will produce the random function each time it is run, rather than on what day it is run. I don't think you would be able to do that with a SQL query.
More than likely, you would need to create a new table in your database that acted as a diary. Each row of the diary would contain a date and a link to a product. This data would then be used to pull back the relevant product for that day.
That is the only way I can see you doing this....