How do I give a role permission to set a site variable? I have a custom variable in one of my modules and I want to be able to give permission to that variable to a specific role on my site.

I have the hook_permission function setup and I can see it in the admin/people/permissions interface, but I'm not sure how to implement a hook or whatever to give the user access to admin/config/system/variable/edit/my_custom_variable
One method would be to use something like https://drupal.org/project/config_perms to add a custom permission to the admin/config/system/variable/edit/my_custom_variable path. You can then use this custom permission to grant access to it.