One not so great method would be to limit the amount of uins they can add to their list. With this method you could have perhaps 5 columns (avoiding the 'row' problem) in your database table devoted to uins (ie: uins_1, uins_2, ... uins_5). I am sure there is a better way of doing this though.
However, there is probably a way to do this using multiple entries in a single row (as u are suggesting) perhaps by dictating what seperates each entry by a special character (ie: a comma) and using 'ereg_replace' to convert that special character to web based readable output?