Mrs.marie, your daughter can apply for Business Visa (F visa)which can be issued to aliens coming to China for intership for less than 6 months, but she should have one of the following documents:
a. Authorized Notification Form for Visa Application issued by competent Chinese authorities (government or its foreign affairs and trade commissions) on both the national and provincial (provinces, municipalities and autonomous regions) levels (original or fax).

b. Authorized Notification Form for Visa Application issued by Chinese enterprises or public institutions duly authorized by competent Chinese authorities (original or fax) and both the original and photocopies of business license or business approval letter carrying the name of the applicant who has investment in or operates the business in China.

c. Invitation letter (original or fax) from a branch of the applicant's company in China.

d. Invitation letter/card (original or fax) from competent national authorities in China, local governments at township level or above, Chinese companies, enterprises or public institutions.

Otherwise, she can only apply for tourist visa (L visa), she can ask for 43 days or more stay duration in China, for more information, please refer to http://ca.china-embassy.org/eng/lsfw/Chinese%20Visa/t37727.htm