I get the information from the official website of Chinese Embassy in Singapore: Non-Singapore citizens shall provide documents that entitle them to reside for an extended period of time in the Singapore, such as a PR, WP, EP, STP, DP. Temporary visitors to Singapore should apply for a Chinese visa in their own country. For the special case, the visa officer has the rights to make the final decision on whether issuing a visa or not.
Therefore, I'm afriad that you can't get get the Chinese visa from Singapore.