Yes, you can apply for a visa to China in Italy. Please check the consular districts of Chinese embassy and consulates. The required documents are as follows:
1. Original passport remaining to be valid for at least six months from the date of application and with sufficient blank visa pages.
2. One completed Visa Application Form with a recently-taken passport photo stuck on it.
3. Return ticket or hotel order in china.
4. Original and a copy of your permanent residence or work permit which should be valid for at least half a year in Italy.