How Do You Get White Nail Polish Off A Black Leather Sofa Without Damage?

Use nail polish remover and then use black shoe polish to help to put back the original black color in the couch.

Please do not use nail polish remover.  This is a solvent and will also remove colour/finish from the leather itself.  If the nail polish will not carefully peel off the leather then the repair is best left to a leather specialist who will be able to remove it and/or replace any finish and colour that is required.  If you use boot polish on a leather sofa it will come off on your clothes - best to let someone use professional repair products to get the job done properly.
DIY colour off the internet generally does not work and can cause expensive repairs to be needed.
Using household products can lead to bigger problems which will then be very costly to fix.
Damage to the leather finish cannot always be seen with the naked eye but in the long term can lead to major problems.