I had the same problem, it appears (well for me anyway) I can only delete a song from the main library not from playlists. In the new version if you go to the songs tab then find the song - command click the drop down box now has delete or use command delete.
Hope that helps, delayed response but just experienced the same problem!
You need to ensure you have "Manually manage music" ticked on the summary tab. Then apply the change and sync again. Once I did that, I highlighted the two songs I wanted to delete, right clicked and delete came up as an option! Yay!
Hope that helps!