Before answering this question, I just want to confirm that you mean Conservative as in a member of the American political right. If you mean it in some other sense, let me know.
Conservatives probably have plenty to argue with Confucius about, but at their core they share some common premises. They agree that society should be focused on family and tradition, and that humans should work together towards unity.
The most important similarity is the Confucian/Taoist concept of wu wei, or inaction. Confucians and Conservatives alike believe that government is most effective when it does less, ensuring that things work smoothly without dictating the everyday happenings of a country. At the same time, Confucians believe in respecting and obeying the national authority when it does take action, which many patriotic minded Conservatives would agree with.
If you want more ideas for answering this question, get in touch with me. We could research some more specific examples of Confucian policy and see how it compares to Conservative thought!