Not a cPanel user but have seen it some so this from those experiences.
In your 3.7.1 instance turn on file system repository.
Using cPanel's file browser, in the data directory for the 3.7.1 instance, create a directory in 3.7.1's moodle37data/repository directory called 'coursebackups'. The name of moodle37data given here for example ... you adjust.
Note it's full path location ... write it down ... you will need it in the 3.1.x.
Back to 3.7.1's admin interface and finish setting up that file system repository by name of 'coursebackups' and select the directory you made ... 'coursebackups'. Do that in any course you have in the 3.7.1.
Now in the 3.1.8 instance ...
Set up automated backups and set the designated directory to be the full path to the 'coursebackups' directory you made in the 3.7.1's moodle37data/repository/coursebackups
Set the time to run in the near future.
Check your 3.1.x sites backup defaults. All items checked as included ... users, etc.
Your cron job needs to be running on the 3.1.x ... it will run automated backups at appointed time you set up in config of autobackups.
When autobackup finishes running, check with cPanel that there are .mbz files in the repository you set up for the 3.7.1 instance.
OR ... you could make the backups in the 3.1.x, download them, then restore by uploading in a restore process. If there are only a few courses to transfer this might be easiest.
'SoS', Ken