or at least give a Chinese equivalent of a card
India issued to its former citizens

PIO card=Person of Indian Origin card.

http://en.wikipedia.org/wiki/PIO_Card

Person of Indian Origin Card (PIO Card) is a form of identification issued to a Person of Indian Origin who hold a passport in another country other than Pakistan and Bangladesh.

Other conditions are:

person at any time held an Indian passport or;
person's parents or grand parents or great grand parents were born in and permanent residents in India, but not moved to Pakistan and Bangladesh or;
person is spouse of a citizen of India or a person of Indian origin as per above.
It came into force with effect from 15 September 2002.

[edit] Uses
The various benefits available to a PIO cardholders are:

No visa required for visiting India during the period of validity of PIO Card.
Exemption from the requirement of registration if stay in India does not exceed 6 months. Should the continuous stay exceed six months, registration will be required within 30 days of the expiry of six months with the concerned Foreigners Registration Officer.
Parity with non-resident Indians in respect of facilities available to the latter in economic, financial and educational fields.
All facilities in the matter of acquisition, holding, transfer and disposal of immovable properties in India except in matters relating to the acquisition of agricultural/plantation properties.
Facilities available to children of Non Resident Indians for getting admission to educational institutions in India including medical colleges, engineering colleges, Institutes of Technology, Institutes of Management etc. under the general categories.
Facilities available under the various housing schemes of LIC, State Governments and other Government agencies.
Persons with a PIO are not

allowed to vote
eligible for an inner line permit. They have to apply for a Protected area permit.