While you're reading my answer, take a look at top R side of your screen. You will see word: 'Jobs'  very close to the word 'Classifieds'. Click on 'Jobs'. Now, you are on new page. Look on top L side. It is written: Location --->All Cities. Write in 'Nanjing', and click 'go' button.

You can also go for a walk, and ask for job at Training centers in the City.

Good luck!

first off many people won't hire desperate people and "I need a job a teaching"? Just make a resume and send it out by email to certain schools not all the schools. 

thebeijinger.com > classfieds> 
there are loads of teaching jobs available. Goodluck

Try anyone of the major agencies if you are really desperate : www.chinabroad.org, www.anesl.com, or www.networkesl.com.  I don't vouch for any of them but the Nanjing job market is both really hot and a little oversaturated (stronger supply than demand) and as a result, wages are considerably less than what they should be.  It's a great city.

Did you find your job in Nanjing or not?  If not, here's an agent that is actually the Jiangsu Ministry of Education.  They are rather good at finding jobs in Nanjings:

Rm: 2301-2302, 15 W. Beijing Road, Nanjing, 210024, P.R.China.

Company Phone Number (with English speaker answering):
025-85150917

Should not be a problem in greeting a teaching job in Nanjing. More so when you are there already. Have contacted any agencies yet?