Sharing files privately individual users I'm trying to create a Drupal 7 feature whereby an admin uploads multiple files that are only visible/downloadable by a specific user. These files would be visible on the user's profile page or (alternative) a document page where a user would only see the files available to them. Ideas?
Drupal private files can only be downloaded by someone who has access to the node the file is attached to.

So you can set up a content type that allow an unlimited number of files attached to a node. Then you set up an Access Control List to that node, where you make sure only the specific user has access to the node.  Let the admin create one node per user, and upload all files to be shared privatly with a specific user to the user's node.

To mange access control lists to nodes, you can use Flexi Access module.