If your software does not run without those files, you will have a problem with any kind of deployment, manual, automatic or continuous, with any kind of VCS, or even without any VCS. So either change your software so that it can run actually without those files (for example, it could assume some kind of "default parameters" if the files are missing), or you provide some version of those file suitable for deployment which are copied (as part of the deployment step) to the destination environment in case there is no "private" version of those files in place.
If you are talking about something like a file containing database credentials to logon to the server, which, for security reasons, you do not want to be in version control, then you will have to put that file into the deployment environment once, probably manually, by a person which has enough rights or knows the password. But that is intentional and should not stop you from deploying daily new versions of your software. Just make sure a credentials files in place is not overwritten when you deploy a new version.