Hong Kong is your best bet.... download the forms then it will be faster there, there are allways many people who aply there.

You may wish to try one of the bigger travel agencies in Taipei.  In the past, they would collect foreign passports, ship them to Hong Kong, have the visa issued in Hong Kong, and then return the passport to the holders.

Sometimes, however, the Chinese government has required of holders of other than Taiwan passports that these people actually apply in Hong Kong for visas.

Your best bet would be to check with the larger travel agencies in Taipei.

Look here please:

http://www.hftravel.com.tw/
http://www.edison.com.tw/
http://www.settour.com.tw/
http://www.cheery.com.tw/
http://www.eztravel.com.tw 

Please keep in mind the following points when thinking where to apply for a visa:

1.- Sometimes, Chinese officials will ask you to return to your country of origen in order to apply for a new visa.  At other times, they will just grant you one, but it will be a minimal, like 6 moths tp, one or two entries only, and 30 days stay.

2.- Politically, Taiwan is not one of the best places to ask for a visa.  Not the cheaper to go and stay for a few days.

3.- Vietnam (Hanoi) and Thailand are in a way closer, and cheaper (in my opinion) to go and stay a few days to get a new visa.

And if I were in your shoes, I will not go anywhere without first contacting an visa agency and making sure they can get for me the visa I want with the times I request.  Otherwise, you may waste a trip, and time and money