There's nothing mysterious about paper stainers - they simply printed wall paper. They were found in most of the larger towns - there were several in competion with each other in Leeds by the 1820s, for example.
It seems to have emerged as a distinct trade in the mid 1700s. Prior to that only the very wealthy had wall paper, from China, France or perhaps London. The paper stainer block-printed the paper by hand on relatively short lengths of paper. There was a register pin set in each corner of the wooden block (which they carved themselves) to help locate the second and subsequent strikes accurately, and in this way a repeat pattern was achieved. The paper might then be overprinted in a second or third colour in just the same way. They typically hung the paper for customers as well. A good provincial paper stainer would offer London and even French papers as well as his own.
Until 1836 each sheet was taxed, and paper stainers also had to purchase a licence. Sadly, The National Archive assures me none of these taxation records have survived.
By the mid 1800s the paper stainers were being driven out of business by rotary-printed paper in long rolls, printed from engraved metal plates, as we know it today. My Hargrave ancestors printed wall paper in Leeds in the traditional mannner for 65 years but called it a day in 1847. Two other paper stainers went bankrupt in Leeds in the late 1840s - a sign of the times, perhaps - though some struggled on. A handful of people around the world have revived the craft and are producing wall papers in the manner of the old paper stainers.