Which module will allow a user to grant another user permissions for editing content of content type
If those are existing permissions on your site already and you just want to control delegation, it sounds like you might want the Roleassign module. 


  RoleAssign specifically allows site administrators to further delegate the task of managing user's roles while withholding the Administer permissions permission.
  
  RoleAssign introduces a new permission called Assign roles. Users with this permission are able to assign selected roles to still other users. Only users with the Administer permissions permission may select which roles are available for assignment through this module.


If that is not sufficient for your needs, a combination of Roleassign and Workbench Access would likely serve your needs. 


  Workbench Access creates editorial access controls based on hierarchies. It is an extensible system that supports structures created by other Drupal modules.
  
  When creating and editing content, users will be asked to place the content in an editorial section. Other users within that section or its parents will be able to edit the content. A user may be granted editorial rights to a section specific to his account or by his assigned role on the site. 


A combination of these two modules would likely be more than adequate for your purposes.