Nanjing weekly metro ticket

No, there is no One week subway pass.
Currently, two kinds of card for foreigners are the following: Single Journey Tickets and Public Transportation Card (called 'Jin Ling Tong in Chinese).
So according to your situation, Jin Ling Tong is a suitable choice for your 7 days stay. It can be purchased for a refundable fee of CNY 25. And the initial stored value is CNY 50.
This transportation card can be widely used to the city transportation, such as subways, public buses and several taxis.

Hi Jerome
Very useful thanks. Found a kiosk in Xinjiekou metro station and the attendant seemed to know exactly what we wanted as we approached asking for 75Y and showing us a card. First impressions today are very positive, frequent trains, good signage.
Thank you for your help.
Colin