Technically there is no feature to upload contacts to the unsubscribe list. However, there's a simple workaround.
Step #1 - Create the csv file with your blacklist
Create an import csv template with your blacklist. Make sure you follow the correct file requirements. If you have no idea what we are talking about, check out this article.
Step #2 - Upload the contacts to your SMS Central account
Once you have the file, upload the contacts into a NEW GROUP (make sure you check the "Create a New Group" checkbox).
Name this group something like "Uploaded Unsubscribed" or any name that will be easy to remember.
Step #3 - Bulk-Unsubscribe them!
Go to Contacts > Contact Group (in this example, click on "Uploaded Unsubscribed").
Select all your contacts and blacklist them. For more info on how to bulk-unsubscribe, please read this article.
Voila! All these contacts are now unsubcribed.
To keep a clean and organised database, we suggest once you have unsubcribed these contacts, you delete the group.