Cpanel provide JSP, Servlet support with Tomcat. This is available as Addon Modules. To install tomcat, do the following.

1. Login to your WHM as root
2. Under Cpanel > Addon Modules find "tomcat", you need to check the check box saying "Install and Keep Updated"
3. Go to bottom of the page and click "save" button. This will install Tomcat on your server.

After installation is finished, it will provide you admin login details

            Installing starttomcat and stoptomcat files...Done
            Adding TomCat user...Done
            Adding includes to httpd.conf...Done
            Adding TomCat to chkserv.d...Stopping chkservd: [  OK  ]
            Starting chkservd: [  OK  ]
            Done
            Setting up the web.xml...Done
            Setting up rc.local...Done
            Finishing Install...Downloading mysql-connector-java-3.0.15-ga-bin.jar...
            Done
            Restarting httpd.../etc/rc.d/init.d/httpd start: httpd started
            Done
            Starting TomCat...Scanning httpd.conf
            Done
            Install Complete
            The admin url is http://server10.hosthat.com:8080/
            The admin user is root
            The admin password is Hsgh12345h
            

Now tomcat is installed on your server, close your WHM and start again, may be you need a refresh to see the changes in WHM, there will be some new options in WHM left side menu.

            Account Functions > Install Servlets
            Restart Services >  Servlet Server (tomcat)