"BY virtue of an execution issued out of the supreme court of judicature of the state of New York, and to me directed and delivered against the goods and chattels, lands and tenements of David Terry, I have seized and taken all the right, title and interest which the said David Terry has in and to the following described lots of ground, lying and being in the village of Greenbush [now City of Rensselaer], lots numbers forty-two, forty-three and forty-four, forty-two feet front and rear, and two hundred feet deep, bounded on the north by Third street, east by lot number forty-five, south by an alley, and west by lot number forty-one; also two lots numbers eleven and twelve, fifty feet front and rear, and one hundred and twenty feet deep, and bounded on the south by Mechanic street, east by lot number thirteen, north by burying ground lot, west by lot number ten, which shall expose to public sale on the third day of February, eighteen hundred and thirty-eight, at two o'clock in the afternoon, at the public house of Evert Wynckoop, in the village of Greenbush.—Dated Greenbush, December 19, 1837" (emphasis added)
"AUGUSTUS FILLEY, Sheriff.
"By. L. RYSEDORPH, Deputy."
Troy Daily Whig. December 19, 1837: 2 col 5.

"Cemetery" at end of driveway (now the one-lane Plum Street) off Mechanic Street (now Third Avenue) on inset Greenbush map.
Map of Rensselaer Co., New York. Philadelphia, PA: Smith, Gallup & Co. Publishers, 1861.

"Cem." at end of driveway (now the one-lane Plum Street) off Third Avenue.
Beers, F. W. "." Atlas of the Hudson River Valley. Watson & Co., 1891

A playground and park and (possibly parts of Plum Street) were placed on the site of the cemetery sometime before 1933.

"City Engineer John E. Quinn was directed [...] to grade the Third Avenue playground and erect a wire fence around the grounds."
"Bids Accepted in Rensselaer Council Work; Long Session in Awards for Contracts Totaling $14,636." Albany Evening News. April 19, 1934: 12 col 1.

It has not yet proven possible to find any record of the cemetery having been moved. The cemetery is still identified as a cemetery on the current tax map, a lot just over an acre in size.

City of Rensselaer Tax Map 143.76 (page 33 of 63)