Can I get there a tourist visa for China as a foreigner?

I'm afraid that your application will be denied. An applicant holding a passport other than Indian passport should provide the original and a copy of their permanent residence or work permit which should be valid for at least half a year (except for those who are visa or permit exempt for residing or working in India);

You can try to call the China Visa Application Service Center in Mumbai to enquire it.
Address: 4/18, Tulsiani Chambers, Free Press Journal Marg, Nariman Point, Mumbai
Tel:+91-22-22855271 Fax:+91-22-22853923