EC2 Update my existing AMI

You could update your configuration with a user-data script that is run when you launch your instance.

What you put in the script depends on how you manage your configuration at the filesystem level. I personnaly put my configuration files in a Mercurial repository and simply do a pull to update it.

It is not possible to update an existing AMI and keep the same AMI id. You will either need to create a new custom AMI and update your launch configuration for the Auto Scaling group, or change your setup to apply changes to the instance after launching an instance of the base AMI as @DavidLevesque suggests.

It is a common architecture to download application, configuration, and data from, say, S3 on launch.