Inserting the following variables into your settings.php will make them available to Drupal's translation system:

/* User_relationships */
'user_relationship_mailer_request_subject',
'user_relationship_mailer_request_message',
'user_relationship_mailer_cancel_subject',
'user_relationship_mailer_cancel_message',
'user_relationship_mailer_approve_subject',
'user_relationship_mailer_approve_message',
'user_relationship_mailer_disapprove_subject',
'user_relationship_mailer_disapprove_message',
'user_relationship_mailer_remove_subject',
'user_relationship_mailer_remove_message',
'user_relationship_mailer_pre_approved_subject',
'user_relationship_mailer_pre_approved_message',
'user_relationships_ui_msg_submitted',
'user_relationships_ui_msg_accepted',
'user_relationships_ui_msg_disapproved',
'user_relationships_ui_msg_cancel',
'user_relationships_ui_msg_default',
'user_relationships_ui_msg_removed',
'user_relationships_ui_msg_pending',
'user_relationships_ui_msg_pre_approved',
'user_relationships_ui_msg_too_many_relationships',
'user_relationships_ui_msg_existing_request',
'user_relationships_ui_msg_existing_relationship',
'user_relationships_ui_msg_not_accepting_requests',
'user_relationships_ui_msg_self_request',
'user_relationships_ui_msg_non_existant_user',
'user_relationships_ui_msg_non_existant_type',
'user_relationships_ui_msg_unknown_error',
'user_relationships_ui_msg_relationship_type_not_set',
'user_relationships_ui_msg_relationship_type_not_allowed',
);

For more information on when, where, and why to use these please visit the Multilingual Variables documentation.