I cannot answer any questions on why coffee would not be accesible to poor Dutch farmers. However i can provide a couple of (Dutch) sources as to what the replacement beverage would be.

That beverage would probably be "chichoreikoffie" or chicory coffee, it also had other names like "peekkoffie". In 1775 two french doctors supposedly made a cafeïne free beverage brewed from roots. This is where the word "peekkoffie" originates, since "pee" is an old Dutch word for root.

The preacher J.H. Nieuwold (1737-1812) was the first person to cultivate the roots in the Frisian town of Warga. Earliest account of actual factories producing Chichorei stems from 1820 where Teunis Tencate started producing the beverage in what is now the "Abraham ten Cate" street in Borne, Overijssel.

The potato eaters was made in 1885 so that would put chichoreikoffie well within the timeframe for being a substitute for actual coffee for poor Dutch potato farmers.

Sources (in Dutch):

Takes from Borne history:

Harten-Fransen, M.G.E. van, Grepen uit de historie van Borne, deel 2 (Borne 1987)

Chicoryproduction in Borne:

Hulshoff, A.L." De Chichoreifabricage van Theunis Tencate in Borne", in: Jaarboek Twente 1989.

Borne Chicory industry:

Velner, J.A.L, "Bornse Chichorei Industrie", in: Borne, Historie en volksverhalen (Borne 1987) (Borne history and folk tales)

I hope this answer is in depth enough as to what the beverage might be. I came across these sources at www.entoen.nu a collective part of the Dutch Canon, an initiative to preserve Dutch History.

Edit: I should clarify here that J.H. Nieuwold was not the first to cultivate the roots, but he was the first to do so in what was then the Republic of united Netherlands.