Cover versions can always be made under a compulsory license; you have to pay the songwriter, but they can't say no.
So recording a version with a separate vocal track is 100% doable for any song.
However, to actually use it in Karaoke, it's no longer just a cover; even though it's just the words that are shown along with it, it's part of a larger work, so you need the same sort of license you would need for using it in e.g. a TV ad, and that needs to be negotiated with the copyright owner.
[edit]
For more details google "mechanical license" and "synchronization license"; the first is the "I want to record a cover" and the second is what you would need for using in karaoke.
So recording a version with a separate vocal track is 100% doable for any song.
However, to actually use it in Karaoke, it's no longer just a cover; even though it's just the words that are shown along with it, it's part of a larger work, so you need the same sort of license you would need for using it in e.g. a TV ad, and that needs to be negotiated with the copyright owner.
[edit]
For more details google "mechanical license" and "synchronization license"; the first is the "I want to record a cover" and the second is what you would need for using in karaoke.