mysql alter int column to bigint with foreign keys

Even with SET foreign_key_checks = 0, you can't alter the type of the constraint column. From MySQL doc : http://dev.mysql.com/doc/refman/5.5/en/innodb-foreign-key-constraints.html

However, even if foreign_key_checks = 0, InnoDB does not permit the creation of a foreign key constraint where a column references a nonmatching column type.

So, I agree with the comment of Devart. Just drop it and create it again.

I could suggest you to rename such fields in GUI tool - dbForge Studio for MySQL (free trial edition):

Just select the field you want to rename in the Database Explorer, click on Refactoring->Rename command, enter new name in openned window, and press OK, it will rename the field and recreate all foreign keys automatically.