Users that can add other users in drupal 7
There's a module for that: Administer Users by Role.


  This module allows site builders to set up fine-grained permissions for allowing users to edit and delete other users — more specific than Drupal Core's all-or-nothing 'administer users' permission. It also provides and enforces a 'create users' permission.
  
  To use this module:
  
  
  Create a role for the users who you'd like to be able to create/edit/delete other users
  Give that new role the 'administer users' permission and give it the desired Administer Users by Role permissions
  


I'm using it exactly for the same purpose you described.