Use an update based on a join. Or of you are on 2008, use MERGE. Examples:

USE tempdb
DROP TABLE p
DROP TABLE c
GO

CREATE TABLE p(oldkey int primary key, newkey char(1) unique)
insert into p (oldkey, newkey) values(1, 'a'), (2, 'b')
GO

CREATE TABLE c(oldkey int references p(oldkey), newkey char(1) NULL)
insert into c(oldkey) VALUES(1), (2)
GO

SELECT * FROM p
SELECT * FROM c
GO

UPDATE c
SET c.newkey = p.newkey
FROM p INNER JOIN c ON c.oldkey = p.oldkey

SELECT * FROM p
SELECT * FROM c

--2008 alternative:
MERGE c
USING p ON c.oldkey = p.oldkey
WHEN MATCHED THEN UPDATE SET c.newkey = p.newkey;