What is the optimal way to upgrade production RDS instance?
Upgrading an instance in RDS means RDS will be physically migrating the database to a new instance, likely on a different physical host, so downtime would not be avoidable.  Migrating to provisioned IOPS would likely mean your data would be migrated to a new EBS volume (and the server might be migrated to a new instance as well with this change, depending on whether, internally, machines capable of accessing EBS volumes with provisioned IOPS are physically segregated from machines that aren't, so that they can be on a different class of network hardware) so downtime would again be inevitable.
There appears to be a way to avoid this disruption: a Multi-AZ deployment, which creates an invisible and inaccessible (to you) replica in another availability zone within the region.

In the case of system upgrades like OS patching or DB Instance scaling, these operations are applied first on the standby, prior to the automatic failover. As a result, your availability impact is limited only to the time required for automatic failover to complete.
— http://aws.amazon.com/rds/multi-az/

That should provide a quick and seamless migration path, though I have not had occasion to test this capability.  &quot;Modify&quot; in the console appears to allow you to convert an instance to Multi-AZ.  Presumably, this would result in brief I/O freeze as the instance is cloned, so I of course would recommend testing all of this functionality before trying it.
Alternately, RDS supports an internal mechanism that should allow you to emulate the &quot;add slave; promote to master; switch clients&quot; operation, and this also should allow you to achieve a near-zero-downtime conversion:

Create an actual RDS read replica of your database with the desired instance class
Wait for the replica to come online and be synched with the master
Modify the replica's configuration to add Provisioned IOPS
Wait for the replica to come online and be synched with the master
Verify that both systems have identical data using 3rd party tools
Disconnect your application from the old master
Verify matching binlog coordinates on master and replica to assure that all application writes have replicated
Split the systems with &quot;Promote Read Replica&quot; on the new replica in RDS
Connect your application to the new master

http://aws.amazon.com/about-aws/whats-new/2012/10/11/amazon-rds-mysql-rr-promotion/