From 1763 he studied at the Lyzeum in Schmalkalden. In 1768 he succeeded his teacher Johann Nikolaus Tischer (1707-1774) as organist in Schmalkalden.
He later continued his musical studies with Carl Philipp Emanuel Bach and Johann Philipp Kirnberger. Vierling died in Schmalkalden. Vierling composed several collections of easy organ pieces, a four-voice organ chorale book (1790) and cembalo music such as two trios, one quartet and six sonatas.
Two handwritten annual volumes of Kirchenkantaten are preserved.
He also published a handbook on the art of basso continuo, "Allgemein faßlicher Unterricht im Generalbaß". Among Vierling"s students was Johann Christian Friedrich Hæffner, who became a famous musician in Sweden.