You could setup a condition based on post ID:
<?php if (is_page(12) || $post->post_parent=="12") { ?>
<ul>
Your Menu
</ul>
<?php } else { ?>
<ul>
Another Menu (or put nothing here)
</ul>
<?php } ?>
If you don’t know how to locate the post ID:
“Roll over any page, post or category with your cursor (while logged in and in the “manage” area of course), and the page, post or cat_id number appears in the progress bar in the bottom of the browser.” – http://wordpress.org/support/topic/where-is-the-post-id-number
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