How to auto replicate specific columns only from a table in MySQL
Why not create one separate db for your SSO, which is accessible for each site?
Copying data around will create problems when two sites are editing "the same field".

If you only want to use a copy to set up, you could:

CREATE TABLE newdb.users LIKE otherdb.users;
INSERT newdb.users SELECT * FROM otherdb.users;


If you really want to continuously synchronise tables between databases, you will have to do it with a custom script.
Most important to consider in that case, will be the question of what to do when conflicts arise?
But I would really consider creating one specific db for SSO.