I know that this is an endless topic but here are my two cents:
A pinned Discover Weekly playlist with a download button that would refresh itself in the beginning of each week deleting the downloaded songs. The songs of the playlist would be added to a list that removes the songs on Monday 00:00. If the user has a song already downloaded the list would tag that song as such and not add it to the list of to be removed songs.
Adding songs to liked songs would work as it is because this is only make it easier to listen to the DiscoverWeekly list offline.
Personally I would also love the option to automate the downloading for each week, but I understand that people might not agree with me.