There are two types of copyright, the copyright in the songwriting and the copyright in the recording. When you cover a song, record it, and sell it, you don't need to get permission from the songwriter so long as the songwriter's half of the royalty gets paid every time the recording is sold/broadcasted. Youtube basically tries to do the same thing, if the copyright holder claims your video, then there is a revenue sharing scheme that the parties can participate in to deal with the respective rights of the songwriter and the performer.
Short answer, you can make money on cover songs, on Youtube or anywhere else, so long as the songwriter gets half. That is the law. Youtube tries to abide by this law through its internal mechanisms, but Youtube is generally pretty bad at managing copyright claims, so YMMV with monetizing your particular cover song videos.
Monetizing eligible cover videos - YouTube Help
Short answer, you can make money on cover songs, on Youtube or anywhere else, so long as the songwriter gets half. That is the law. Youtube tries to abide by this law through its internal mechanisms, but Youtube is generally pretty bad at managing copyright claims, so YMMV with monetizing your particular cover song videos.
Monetizing eligible cover videos - YouTube Help