It appears no such a graduate program. At least two years ago when I applied
the nutrition graduate programs I did not see such a program.Some medical
centers associated to universities may have clinical nutrition divisions but
they do not offer graduate program in clinical nutrition or even nutrition.
Some graduate programs in nutrition have faculty doing the clinical
nutrition things but I do not think there is a clinical internship for them.
However you may consider dietetics, there is a program called dietetics and
internship is required for compeletion to be the Registered Dietitian. It is
possible to find a dietitian internship in hospitals where you may be
involved in clinical nutrition.
Here is the official link to search hospitals providing dietetics internship: http://www.eatright.org/students/education/di.aspx