Well it did not fail me.

All the 2 links below identify one "Tanaro" as an Italian Navy tanker sank in January 1943 by a British destroyer.

http://books.google.co.uk/books?id=XDqBUqnrFLYC&pg=PA104&lpg=PA104&dq=italian+navy+ship+tanaro&source=bl&ots=yY1FvOjcbo&sig=qAykYJFHkMgYdzzqtFfSgwqOoZM&hl=en&sa=X&ei=LFh8U_LSBcyXuATnhIKYAQ&ved=0CDAQ6AEwAA

https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0CDMQFjAB&url=http%3A%2F%2Fen.wikipedia.org%2Fwiki%2FHMS_Pakenham_(G06)&ei=LFh8U_LSBcyXuATnhIKYAQ&usg=AFQjCNGuDSeYryVhHo01WGLM-gqAjEB86Q&sig2=aFBwjCB6cp3klZHz4IBZsQ&bvm=bv.67229260,d.c2E

There is another TANARO built in the US and later transferred to the Italian Navy where it served as a "Water Carrier" and it likely to be the candidate you are looking for, check page 5. It does not mention the year of building nor when it was transferred but looking at the other vessels in the document all suggest somewhere along the fifties.

http://www.filtcgilfoggia.it/notiziari_filt/2009/165/All165MAR1.pdf

Once you have this all you need to do is accessing the Italian Navy official web page and contact them, I am sure they have a historical records office like most navies and armed forces in the world, they should be able to help.