If your connections happen with distinct database roles (logins) that can be tied to a timezone, then PostgreSQL offers a simple solution:
ALTER ROLE my_role SET TIMEZONE = '+1';
Every connection initiated with this role will operate in its preset timezone automatically (unless instructed otherwise).
Note that, quoting the manual:
This only happens at login time; executing SET ROLE or SET SESSION AUTHORIZATION does not cause new configuration values to be set.
And you may want to use a time zone name instead of the plain offset to follow DST rules and other political manipulation of the local time. More:
Alternatively, you could create a look-up table for your logins where you store the respective time zones (which might serve additional purposes):
CREATE TABLE usertime(username text primary key, timezone text);
-- careful, "user" is a reserved word (but "timezone" is not).
INSERT INTO usertime VALUES
('postgres', '+4')
,('my_role' , '+3');
Write a tiny SQL function:
CREATE FUNCTION f_user_ts()
RETURNS timestamp AS
'SELECT now() AT TIME ZONE u.timezone
FROM usertime u
WHERE u.username = current_user
' LANGUAGE sql STABLE;
Now, this returns the local timestamp for the current role (user):
SELECT f_user_ts();
More info
See the fine manual for the AT TIME ZONE construct. Both of these syntax variants are valid:
SET TIME ZONE TO 'UTC';
SET TIMEZONE TO 'UTC';
But now() AT TIMEZONE foo; is not! It has to be:
SELECT now() AT TIME ZONE foo;
foo being a text variable (or column like in the function above) holding a time zone offset, abbreviation or name. You can also supply a string literal directly.