The methods previously given are very good.  I have only a few additions.

If the damage is really severe, automotive two-part "bondo" filler is
a good choice.  For small spots, a lacquer-based spot putty would be
quicker and compatible.

I have used several black automotive lacquers and found R&M (Rinshead
& Mason) brand to be significantly blacker than other brands.  When I
have tried to use other brands to repair or touch up something painted
with the R&M material, they look only dark gray against the R&M black
lacquer.

This finish is extremely easy to maintain if the original materials
are used.  When a small area is damaged, only that area needs to be
refinished.  The repair will blend in easily with the original finish
once it is thoroughly dry.  I believe this is the primary reason that
satin finish black lacquer is the choice for professional pianos that
have to be moved often.

Karl Petersen
Meridian, Idaho