Delete rows with foreign key in PostgreSQL

To automate this, you could define the foreign key constraint with ON DELETE CASCADE.
I quote the the manual for foreign key constraints:

CASCADE specifies that when a referenced row is deleted, row(s)
referencing it should be automatically deleted as well.

Look up the current FK definition like this:

SELECT pg_get_constraintdef(oid) AS constraint_def
FROM   pg_constraint
WHERE  conrelid = 'public.kontakty'::regclass  -- assuming public schema
AND    conname="kontakty_ibfk_1";

Then add or modify the ON DELETE ... part to ON DELETE CASCADE (preserving everything else as is) in a statement like:

ALTER TABLE kontakty
   DROP CONSTRAINT kontakty_ibfk_1
 , ADD  CONSTRAINT kontakty_ibfk_1
   FOREIGN KEY (id_osoby) REFERENCES osoby (id_osoby) ON DELETE CASCADE;

There is no ALTER CONSTRAINT command. Drop and recreate the constraint in a single ALTER TABLE statement to avoid possible race conditions with concurrent write access.

You need the privileges to do so, obviously. The operation takes an ACCESS EXCLUSIVE lock on table kontakty and a SHARE ROW EXCLUSIVE lock on table osoby.

If you can’t ALTER the table, then deleting by hand (once) or by trigger BEFORE DELETE (every time) are the remaining options.