I don't know how to say this tactfully but if you are restoring
a player piano and not just "making it work," then _please_ use the
same type screw as was originally used, particularly if is a rare
coin-operated piano or reproducing piano.

Dry wall screws are just not correct.  First, they were never used;
second, they do not have the strength of a wood screw -- they are for
holding drywall not for furniture repairs.  There are special deep
thread screws that appear to look like drywall screws used by modern
furniture manufacturers that have a larger root diameter with deep
threads.  These are not suitable for antique player pianos.

Phillips head screws did not come into use until sometime around
World War Two, long after the heyday of the player piano.

The first posting that suggested using CA glue on a Q-tip swab was
probably the best advice.  If the hole is beyond that as a repair then
a dowel cut with a plug cutter so the grain is correctly orientated
would be my choice.  An invisible repair is optimal.

Another choice, if possible, would be to drill a hole so a store-bought
maple dowel can be inserted with proper grain orientation.  Never try
to have a dowel hold a screw in the end grain.  Take a handful of
drinking straws in your hand and notice how easy it is to push the
straws in the center out of the bundle.  That is the same as putting
a screw into end grain.  The instances you do see screws in end grain
are usually in low stress areas.

Don Teach
Shreveport, Louisiana