I don't want to use the popular function for sites which are getting the most hits. Instead there are certain 'partner' sites which I want to mark as popular, is it possible to do this?

I seem to remember it was a simple switch in Links2?

All you really need to do is add a new field to the table
Database >> Links >> Properties (call it isSponsored, set the default to no, and then change the ones you want to be sponsored to yes) and then in Options define the category sort order as "isSponsored (not sure if it's DESC or not, but won't be too hard to do via trial and error), Title".