Canadian driving Belgian car in Italy--is it possible

If it's a private agreement - i.e. you are borrowing somneone else's car, not a rental car, you should have a letter from them authorising you to drive the car (preferably in Italian, or in English), plus you need an insurance certificate which clearly covers you. You will also need the car's registration papers.
With your driving licence, letter of authority, insurance and registration papers plus your passport, you should be fully covered. Italian authorities sometimes require an IDP from US drivers, so check with Italian consulate about Canadian licence holders.

Insurance companies across the EU issue an international insurance certificate (known as "green card"), which is often included in standard insurance contracts and extends car insurance for driving it into a wide list of countries. The problem is checking the insurance conditions about WHO is enabled to drive that car. Conditions about that point can vary in a wide range.

I have been fortunate enough to be able to borrow cars instead of renting several times. As long as you have proof of insurance you should have no problem. I would get your relatives to check with their insurance carrier though, driving in Italy has some special insurance requirements. If language is no issue, there should be no problem for you. Also, go to the nearest CAA office and get an International Drivers License.