The traditional term for this product is 'Leatherette paper'.
The stuff suitable for piano roll boxes is becoming ever-harder to
find.  Bookbinding suppliers seem the best source.

When I started making rolls I got a sample book with about 200
patterns or colours.  The late Richard Vance, who made superb boxes,
was most impressed with this when he visited me.  He'd failed to
locate any American supplier to private buyers, so went to the firm,
bought a block of 250 sheets and posted it home.  He said the place
was run by an elderly couple.

So, I wasn't greatly surprised when my box-maker told me the firm had
sold up.  The new owner has whittled down the range by not restocking,
and is down to about a dozen options.  I'm working my way through the
remaining stock of red 'Alligator paper'.  It's grown so hard to source
that my box maker -- in business since the 1880s -- has asked _me_ where
to find it!  Nobody uses the old patterns; I'm told the market is now
for gaudy finishes, mostly for things such as notebooks and diaries.

One of the large makers of leatherettes is the Fibermark group.  Their
term for the product is 'rigid setup box wrap', for which they have
50 options.  'Acrolin', 'Pellaq' and 'Kivar' look like good roll-box
options.  Some are made in the USA, others in the UK.  These are sold
in industrial quantities as reels of hundreds of feet.  As a random
example, start with

  http://www.fibermark.com/products/acrolin-alligator 

There are no doubt many other similar makers around the world,
typically places with long-established packaging needs such as Europe
or China.  The challenge is to find such paper converted to sheets
for box covering.

This can be done, such as a bookbinding supplier in Germany with online
sales in blocks of 250 sheets.  The basic options seem to come down to
about 70c/sheet, which is about what I've been quoted.  I notice that
many of the options are 'limited' and I suspect the options will
diminish rapidly with time.

https://www.schmedt24.de/en/bookbinding-supplies/papers/cover-papers/leatherette-paper/53/leatherette-paper-with-lizard-emboss?number=1128-012 

https://www.schmedt24.de/en/bookbinding-supplies/papers/cover-papers/leatherette-paper/58/leatherette-paper-with-croco-emboss 

Julian Dyer