I own a Punto ELX W reg and I have a similar noise coming from the rear
suspension. I did quite a bit of reading on this and had the car
checked at a garage and they suggested that because both of the rear
shock absorbers have developed slight rust on the inner tube, this is
rubbing against the outer tube, thus creating this kind of
Apparently, the rattling noise (not the rust) is a common design fault
on all MKII Puntos and whoever discovered this quickly enough had the
whole rear subframe replaced by FIAT under warranty, provided the car
was under 3 yrs old, of course.
The garage told me that it is perfectly safe to drive the car if I
could live with the noise. It does get a bit irritating sometimes,
however, I've lived with it for more than two years now. Because your
Punto makes the noise from only one side, I suggest you make sure that
it doesn't come from the other side, too and if not, then get your
shock absorbers and rear suspension bushes checked for their condition.
If it is the bushes, this is usually a quite inexpensive job. However,
expect to pay a lot more for new absorber(s).