When you go to pick up the vehicle, you will be asked by the company to list all of your additional drivers. They will have to meet the minimum age requirements. One of the few companies that may allow an added driver as young as 18 would be E Z Rent a Car
Many of their locations allow renters to be 18, so they may have more leeway with underage requirements. Their website states that you should check policy for a specific location, which you can find at RentaWreck.com
For other car rental companies that I researched, all additional drivers must be 25 years of age or older, some companies do allow additional drivers between the ages of 21-24 as well. Check out Company Specific Car Rental Additional Driver Policy.
As well as age requirements, there are also licensing requirements as well as credit card requirement for additional drivers as well. These requirements vary by company.
Unfortunately, your son's ability to drive the rental is not based on his coverage under your insurance policy, but by the requirements of the rental company. If you allow an unauthorized (and underaged driver) to drive the rental, you will be violating the terms of your rental agreement.