Is there an update/upgrade of Library Pro Silver that is compatible with Mac OS El Capitan?
I've searched the web, but couldn't find anything related to the availability of an update for Mac OS El Capitan. There was a Reddit post where users talked about it, but nothing official. Therefore, you have two choices now:
Install an older version of Windows through Paralells Desktop and then run the app there.
Use another application that provides similar functions as Library Pro Silver does. Here is the link to the app page: https://www.powerschool.com/products/powerschool-sis/L4U/