How can I fake inet_client_addr() for unit tests in PostgreSQL?
inet_client_addr() is a system information function.
It is located in the schema pg_catalog like other built-in functions (except for additional modules).

pg_catalog is automatically part of the search_path. Per documentation:


  In addition to public and user-created schemas, each database contains
  a pg_catalog schema, which contains the system tables and all the
  built-in data types, functions, and operators. pg_catalog is always
  effectively part of the search path. If it is not named explicitly in
  the path then it is implicitly searched before searching the path's
  schemas. This ensures that built-in names will always be findable.
  However, you can explicitly place pg_catalog at the end of your search
  path if you prefer to have user-defined names override built-in names.


Bold emphasis mine.
So we create a dedicated schema and place it before pg_catalog in the search_path:

CREATE SCHEMA override;

CREATE OR REPLACE FUNCTION override.inet_client_addr()
  RETURNS inet AS
$func$
SELECT '127.0.0.1'::inet
$func$ language sql STABLE;


SET search_path = override, pg_catalog, public;


Then your call finds your custom override-function first:

SELECT inet_client_addr();


SQL Fiddle

Make sure, unprivileged users cannot create objects in the override schema, or they can play all kinds of tricks on you. That's not the case by default. Per documentation:


  No privileges are granted to PUBLIC by default on tables, columns, schemas or tablespaces.


Bold emphasis mine.

Care is needed if the same user should be allowed to create objects in the database.
Per documentation:


  The first schema named in the search path is called the current
  schema. Aside from being the first schema searched, it is also the
  schema in which new tables will be created if the CREATE TABLE command
  does not specify a schema name.


Always specify a schema name for CREATE commands, and disallow crating object to all by default to rule out mistakes.