Umm, let me think... I don't know how it is with your version, but with mine, I think you'd have to write a code on the online page or something like that that for each user displayed, the code will go to the owned_adoptables table and return the count of all adoptable rows that have an owner that matches the user's name. Then, I remember reading a PHP book that tells you how to count rows and order by value, but I have no clue if that'll work with mysidia.
Another much easier way to do this if your site has no pets, is maybe to add a pet count column in the users table and set it to 0. Then, each time a user adopts a pet, add the number of pets adopted to the value. Then do the order thing.
Did that make any sense?
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