"The first Dutch Reformed cemetery was located near the southern side of the city stockade - between today's Beaver and Hudson Streets. Previously, notable members were buried beneath the church.

By the 1780s, the church cemeteries were full and burial places were no longer appropriate for the heart of a developing urban center. At that time, the Albany common council designated a block of land bounded by today's Eagle, Hawk, Lancaster, and State Streets as the city's municipal cemetery. The city plot was apportioned to the four churches and to leading Albany families.

"Churches in Albany before 1776
Dutch Reformed
Lutheran
St. Peters Anglican
Presbyterian

In 1766, the Albany Corporation authorized a German Reformed Church. However, it does not appear to have sustained services until after the Revolution.

By 1800, a Methodist Church and St. Mary's Roman Catholic Church had commenced operations in the city."

With the rapid growth of Albany's population following the American Revolution, the first city plot soon proved inadequate. By 1801, a new cemetery had been opened on public land near the western edge of the settlement just above newly laid-out Washington Square. A few years later, the Eagle Street block was subdivided into lots for development.

Four times as large as its predecessor, the Washington Park Cemetery was bounded by State, Robin, Hudson, and Knox Streets and also was divided into discreet church and family plots. Unlike its predecessor, it included a section for Negroes and another for strangers. Many new graves were created to accommodate the needs of a booming city and to bury those who died during the Cholera Epidemic that swept Albany (as many other populated migration destinations in the United States) in 1832.

Fueled by constant immigration, the city of Albany continued to grow and to expand. By 1818, building lots had been laid out facing Washington Square and now surrounded the cemetery on three sides. By the 1840s, houses were built on those lots. Snipe Street also was extended through the heart of the cemetery. However, the Washington Park Cemetery was used until 1868 when the last remains were relocated to Albany Rural Cemetery. A few years later, the one-time city cemetery was transformed into part of Washington Park."

http://exhibitions.nysm.nysed.gov//albany/dead.html

The current location of any particular grave (and whether it was actually moved) that was buried within the city prior to 1868 is uncertain.