The simplest thing to do is indeed to copy the entire data directory to the new machine. The default data storage directory is C:\\ProgramData\\Red Gate\\DeploymentManager\\Data. The only caveat is that you should make sure the Deployment Manager service is stopped on both the source and target machines before trying to copy the folder (the full name of the service is "Red Gate Deployment Manager").
You can also put the data directory in place before installing Deployment Manager on the new machine, and then specify the path to the newly copied data directory in the appropriate step in the installer (it's the page titled "Database location").
Technical Lead - SQL Source Control | DLM Automation