If you want to backup your iPhone contacts without iCloud then you must give a try to My Contacts Backup, which is an easy to use app and available as a free or paid via App Store.
Backup/Restore iPhone Contacts
Just download and install My Contacts Backup on iPhone then launch it and tap on Backup button. Follow the on screen instructions.
My Contacts Backup will create backup file with .VCF extension, and attach it to send it as an email
Now whenever you need to restore your iPhone contacts, open your email on iPhone, tap on attachement backup file, tap it again to open it, and click on “Add All Contacts” button in its interface and that’s it.
My Contacts Backup is available as a free and paid Pro version, so it all depends on your choice for which you want to go, but free My Contacts Backup works fine if you have no issues with ad-supported free version.
Download My Contacts Backup for iOS [Free]