A search of some of the Olean newspapers on ancestry dot com for the term 'brick yard' mentions three brick companies. It also frequently mentions 'the brick yard' without specifying a company name. Apparently one of the places had a nice pond that locals used for ice skating in the winter.

Allegany Valley Brick Comp, East Olean 1913
Sterling's Brick Company, 1919, later known as Dave Rosen's Brick Co in 1942
McMurray Brick Company, East Olean 1919

There are likely city directories for that timeframe as well.