Yes, it is possible to do this using fine-grained permissions in Active Directory. However, there's a good reason this isn't commonly done.
If you're giving a person the rights to manage user accounts and take backups, that implies a certain amount of trust. If you're only giving them half the rights they need, it's like saying "I don't trust you to do this job, but I'm making you do it anyways."
As an alternative, you could delegate management of a single organizational unit. This way the potential damage is still limited, but now you have a chance to evaluate this person's administrative ability. For more information, try searching Google for "Active Directory delegate control organizational unit".
If you're absolutely set on giving a user the ability to create other user accounts but not delete them, then you'll need to manually edit the ACLs on an organizational unit and grant that user the "Create User objects" privilege.