There are a lot of good reasons not to roll such an airplane.
If the plane has gyroscopic instruments, you might tumble them (cause the spinning gyro to hit the inside of the instrument). This can be expensive.
You might easily over-stress the air frame. Normal category light aircraft are rated to -1.5 to +3.8Gs. (That's for a new aircraft) A botched roll can easily hit 4.5 or higher.
If you over stress the air frame, you might just put a lot of very expensive "wrinkles" in the skin that would be very hard to explain to the FBO, your boss, or the insurance company. Trashing the gyros would be cheaper.
If you're not lucky, the wings fold up and you fall out of the sky. It's a stupid way to die.
Non-aerobatic aircraft typically have limited elevator authority; once upside down, you might find it very difficult to keep the nose pushed up high enough to keep the roll going. Turning a botched roll into a "split-S" is one of the worst "recovery" mistakes you can make, and you're setting yourself up for it.
Non-aerobatic aircraft often have gravity-feed fuel systems. A little bit of 0 or negative "G" and it will get very very quiet in the plane. Some people consider this silence detrimental to the continued safety of the flight.
Non-aerobatic aircraft rarely have inverted oil systems. As the engine gets quiet, it also loses most of its lubrication. Bare metal on metal friction can be detrimental to achieving TBO.
Having said all that, in the hands of an expert, it is technically possible to barrel roll most aircraft.
A good way to tell if you're an expert is to call your insurance company and tell them exactly what you plan to do. If they'll quote you affordable coverage, you might be an expert.
Obligatory links because if I don't include them someone else will:
If you want to roll an airplane, contact your local aerobatic club. In the US and some countries, it's the [International Aerobatic Club]. Get some competent dual instruction in a suitably rated airplane.