I took a quick look at the source code for the Tomcat Manager. It looks like there's a class that's part of the Tomcat source called "Container Servlet". From the javadocs:
A ContainerServlet is a servlet
that has access to Catalina internal
functionality, and is loaded from the
Catalina class loader instead of the
web application class loader.
A ContainerServlet automatically gets passed a wrapper that can be used to get the Context and Deployer -- and the Deployer has helpful methods such as start(String contextPath)
and stop(String contextPath)
that will do what you want.
So, what I think you would need to do is write your own servlet that inherits from ContainerServlet, and configure Tomcat to load your servlet using the Catalina class loader (look at how the Manager is configured to see how). Note that this is probably not going to be an option for you in a hosted environment.
Then your servlet could have, say, a button you press to reload the application. I recommend putting password-protection of some kind in front of that. :)