On page 240 of Frank Sellers' book "Sharps Firearms" there is a photograph of a Model 1974 Long Range No. 1 Rifle in the kind of case you describe. It was made for J.P. Lower, of Denver, Colorado, a dealer and shooter, and presented to him by the company on October 3, 1877. It is attributed to the "George Lower Collection".

The only other illustration of a case I have been able to locate is an all leather scabbard type case made for the Model 1877 Long Range Rifle on page 327 of the same book. Unlike the first case, it has a provision for storing the rear sight separately, rather than leaving it mounted on the rifle. (R. H. Taylor Collection)