You don't have to restart the whole container.
Tomcat supports like the most application servers a feature called "Auto Deployment". The only thing you have to do is copy the war-File into the appropriate folder.
Auto Deploy is turned on with the attribute
autoDeploy=true
on the host tag in your server.xml configuration file.
Default in Tomcat 6 is:
<Host name="localhost" appBase="webapps"
unpackWARs="true" autoDeploy="true"
xmlValidation="false" xmlNamespaceAware="false">
See the Tomcat documentation for various deployment ways:
http://tomcat.apache.org/tomcat-6.0-doc/deployer-howto.html#Deploying%20on%20a%20running%20Tomcat%20server