Try this:
UPDATE business AS b
INNER JOIN business_geocode AS g ON b.business_id = g.business_id
SET b.mapx = g.latitude,
b.mapy = g.longitude
WHERE (b.mapx = '' or b.mapx = 0) and
g.latitude > 0
Since you said the query yielded a syntax error, I created some tables that I could test it against and confirmed that there is no syntax error in my query:
mysql> create table business (business_id int unsigned primary key auto_increment, mapx varchar(255), mapy varchar(255)) engine=innodb;
Query OK, 0 rows affected (0.01 sec)
mysql> create table business_geocode (business_geocode_id int unsigned primary key auto_increment, business_id int unsigned not null, latitude varchar(255) not null, longitude varchar(255) not null, foreign key (business_id) references business(business_id)) engine=innodb;
Query OK, 0 rows affected (0.01 sec)
mysql> UPDATE business AS b
-> INNER JOIN business_geocode AS g ON b.business_id = g.business_id
-> SET b.mapx = g.latitude,
-> b.mapy = g.longitude
-> WHERE (b.mapx = '' or b.mapx = 0) and
-> g.latitude > 0;
Query OK, 0 rows affected (0.00 sec)
Rows matched: 0 Changed: 0 Warnings: 0
See? No syntax error. I tested against MySQL 5.5.8.