According to Descriptions of Occupations: Mines and Mining, the "stable boss is in charge of the stables and of the horses and mules employed at a mine. He sees that the draft animals are properly fed and kept in good condition." The qualifications listed for this job are "[p]hysical strength; good eyesight; good hearing; ordinary ability. A knowledge of veterinary science is advantageous but not essential. He should have had experience as a driver and in the handling of horses."
Albert Parrish was working in Pittsburgh as a "laborer" in 1880, a "stable man (coal)" in 1900, and a "stable boss (coal co.)" in 1910. As the father of 11, he had a lot of children to feed, although four of them died before the age of 5.
There's a great photo on the Historic Pittsburgh website that shows a mule and his driver hauling a coal car from a mine in 1910. The description provides the following information:
"Mules were used exclusively to pull coal cars before mechanized vehicles, because Percherons and Clydesdale horses were too expensive and too large to maneuver in the tight quarters of the mine. Large mule stables or barns were built near the mine to accommodate the animals. Collieries with deep mines had mule stables below the surface where the mules were kept. Every mule driver was held strictly responsible for the safety of all animals in his custody. The mules received medical treatment and were also given frequent rubdowns with horse liniment. A great number of drivers pampered their animals by feeding them sweets such as candy, lump sugar, sweet apples, figs, dates, and cookies. Some drivers even taught the mules to chew tobacco. An Act of Legislature outlawed the underground mule stable in December 1965, making it illegal to house animals in mines."
At the age of 68, Albert was still working but was no longer employed in the mining industry. By 1920, he had moved on to steel. However, his family must have been proud of his former position since his 1924 death certificate shows that one of his daughters indicated his occupation was a stable foreman.