the best method would be to build your excerpt manually (dashboard->Posts->Edit->Excerpt and surround it with a
HTML Code:
<p style="text-align: center;"> ... </p>
The reason for this is that there is no easy way, to determine that a post is to become an excerpt until the actual post content is being processed. But by hand crafting the excerpt, you can set your own justification per post. This way you could have one centered, another right justified etc.