基于其他列组合的MySQL InnoDB自动增量列

I am making a system where users can upload any file they want, and not use it to execute any kind of code. As a part of that, I rename every file, and store its original name in a MySQL table. This table contains the id of the user who uploaded it, and a unique id of the upload. Currently I am doing it like this:

CREATE TABLE `uploads` (
    `user_id` INT(11) NOT NULL,
    `upload_id` INT(11) NOT NULL AUTO_INCREMENT,
    `original_name` VARCHAR(30) NOT NULL,
    `mime_type` VARCHAR(30) NOT NULL,
    `name` VARCHAR(50) NOT NULL,
    PRIMARY KEY (`user_id`, `upload_id`)
) ENGINE=MyISAM;

This means I will always have a unique combination of user_id and upload_id, and every users first upload has an id of 1. However I heard MyISAM is old, and i should rather use InnoDB. Is there any way I can achieve this in InnoDB?

The biggest problem with MyISAM tables is that they are not transactional. From what you say, you will only be creating records and then reading them (possibly deleting them later) but there will be little or no editing. This situation is what MyISAM was designed for, it is fast for mostly read only records. Personally I see no advantage converting to InnoDB.