Shaughnessy Square was a name for the wedge of land, or part of it, between 2nd and 3rd avenues between 105th and 106th streets. In 2016 Golds Auto is on the northern part of the square, the southern tip covered with something like juniper hedges and some brickwork.

Shaughnessy Square.
Recently The Shaughnessy Ice Company erected a handsome office on the plat of ground between Fifth and Sixth Streets at the junction of Second and Third Avenues, Lansingburgh. Alderman Frederick thought the Common Council should take cognizance of the improvement tht has been made and introduced an ordinance, which was passed without a dissenting vote, providing that the plat of ground surrounding the office shall be known as Shaughnessy Square. A petition of property owners was presented asking that favorable action be taken.
“Fight Over Bath; Common Council Has Debate on the Matter of Hours for Lansingburgh’s Cleanup House—Paving of Stow Avenue—Shaughnessy Ice Company Has a Square Named After It.” Troy Times. November 19, 1915: 28 col 2.

To Hoist Flag at Shaughnessy Square.
A seventy-five foot pole will be installed at the southern point of the triangle upon which the office of The Shaughnessy Ice Company are located some time next week, after which a beautiful American flag will be unfurled. There will be no formal ceremonies, however, and it is unlikely that anybody other than the officers and employees of the firm will be present. The Shaughnessy property is the most ideal location for the erection of a flagpole in the entire section, located as it is at the junction of Third and Second Avenues.”
“Lansingburgh.” Troy Times. May 19, 1917: 2 col 5.