I have a running CoreOS instance triggered by AWS CloudFormation. I updated the CloudFormation template via CF designer, but found out that user-data of the existing instance was not updated. Is there a way to update a running (old) CoreOS instance's user-data?
You need to configure the cfn-hup daemon in your template to listen for updates to your instance metadata. This walkthrough shows how you can configure the cfn-hup daemon: http://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/updating.stacks.walkthrough.html
Since you're not using Amazon Linux, you'll probably have to install the Cloudformation helper scripts as part of your initial Cloudformation template as well. You can find S3 locations for those script distributions here: http://docs.aws.amazon.com/AWSCloudFormation/latest/UserGuide/cfn-helper-scripts-reference.html