Hi @michael5,
You shouldn't even need to use the API for this anymore actually. If you take a look at the SIS Import documentation, you'll see you can create a "change_sis_id.csv" file to accomplish this pretty easily.
You'll basically need a csv file with a header line of "old_id,new_id,type" and then for each student you'll have a data line with their old sis_id, the new sis_id, and "user" as the type.
If, for whatever reason, you still want to attempt to do this via the API, it would be the logins method you'd work with. You'd need to list the logins per user to find the login_id with the sis_id you're looking to update, then edit that login to make the change. I had to do this in the past before the CSV method above was introduced, and while it did work out, the CSV method is infinitely simpler.
Hope this helps!
-Chris