I have done exactly what you want to do, and am happy to report that it works. In my first attempts, I encountered the same issue. Make sure that you:
- Create your custom AMI from a running instance of Amazon's beanstalk AMI that you manually launch from EC2, NOT one that was launched from beginning your application through beanstalk. This is vital, as Flashing a beanstalk launched EC2 instance won't work!!
- install Sun's Java as per these instructions, to make sure all the environment and symbolic links are correct. https://forums.aws.amazon.com/message.jspa?messageID=251168#251168
- be patient, as I found for some reason Tomcat takes longer to spin up than with the default OpenJDK config.
If you still can't get it, make sure you check the logs in /opt/tomcat7/logs/catalina.out - I hit a mysterious VerifyException that was resolved by uploading a new .jar to the environment, and that I also ran out of permgen space quickly, which was resolved by upping the values in the 'Container' configuration space of the beanstalk 'edit configuration'.