Unable to add primary key to innodb table without one
You can have an auto-Incrementing column, as long as there is an index (key) on it, to fix this issue you need to execute those commands:

ALTER TABLE my_wonky_table ADD COLUMN count SMALLINT NOT NULL;
ALTER TABLE my_wonky_table ADD INDEX (count);
ALTER TABLE my_wonky_table CHANGE count count SMALLINT NOT NULL AUTO_INCREMENT;
ALTER TABLE my_wonky_table ADD PRIMARY KEY (id, count);