ALTER primary key column from INT to BIGINT in production (MySQL 5.6.19a)
If you have enough space, you can create a copy of the actual table and do the work on that:
CREATE TABLE new_tbl [AS] SELECT * FROM orig_tbl;
Then you can change the column as desired:
ALTER TABLE tbl_name MODIFY COLUMN col_name BIGINT AUTO_INCREMENT;
Once the process is done, you can rename the tables:
RENAME TABLE tbl_name TO new_tbl_name, tbl_name2 TO new_tbl_name2;
Then drop the original table, and you should have the spected result.
percona toolkit is the way to go, at least if you are not super short in time. The conversion took on our table (500Gb, master-slave setup) when we tested it a bit more than 24h, in production it took (with better hardware) almost 1 month (funny sidenote we had about 30 days before we would run out of ids, therefore we started already to plan for plan B and C, working with offline backups, removing slaves,... ). The delay was mainly due to the waiting of the replication happening towards the slaves (we allowed max 50sec time lag). Also make sure to limit the number of concurrent threads. We have more than 2M inserts/day and many million reads.
Also be aware that once the coversion has started you can't stop it (or at least we didn't find any way to restart it) :-(