The truth is that early burial places were scattered around the whole region. For example, Story of Old Allegheny City notes that one hillside "served the first settlers as a common burying ground or Potter's field." There were no members of my clan buried there, I'm happy to report, though there's a good chance I'll end up in a Potter's field myself: As Story of Old Allegheny puts it, a Potter's field is "where the bodies of the poor and friendless & were interred in unmarked graves." The history goes on to note that "Years later, excavations for a street at the foot of the hill exposed the remains of those forgotten unfortunates. Their bones were carefully collected and removed to other cemeteries."
Some neighborhoods may have been settled by the dead long before the living ever moved in. Troy Hill, in fact, was first home to three cemeteries before the living discovered it -- and no doubt there was much spinning in graves and sepulchral moaning of "there goes the neighborhood" when the still-breathing arrived, making all their noise.
But the best known and most important of these early burial grounds was the cemetery between First Presbyterian Church and Trinity Cathedral on Oliver Avenue.
Its use dates back longer than anyone can know for certain. After building Fort Duquesne in 1754, the French realized that the Native Americans had been using the site for a burial ground. In his book Pittsburgh: An Urban Portrait, Franklin Toker surmises, "The burial ground originated in a small hillock that must have been one of the few dry spots in the Triangle when the Allegheny River regularly flooded it each spring." Apparently, the new settlers preferred not to see corpses floating downstream every year. Fussy people, those French. Oliver Avenue, in fact, was formerly known as "Virgin Alley," after a French phrase, Allée de la Vièrge, that reflected its sanctified status as the approach to hallowed ground.
The Trinity Church site was favored by many early Pittsburghers whose names grace city streets and buildings. (You might say -- if you had no respect for yourself whatsoever -- that people were dying to get in.) Many French and Indian War veterans, as well as early leading citizens, were interred there, and some of their gravesites still remain.
There is Oliver Ormsby, for whom Mount Oliver is named, and who laid out much of the South Side. (Sarah and Jane streets are named after Ormsby women.) There is the resting place of Nathaniel Bedford, who helped found the University of Pittsburgh, and Miu-Qua-Coo-Na-Cam, a Shawnee Indian chief whose friends called him "Red Pole." According to his tombstone, his passing was "lamented by the United States," and how many Native Americans can say that?
Like all cemeteries, the place is a bit creepy, but it carries stories of its own, like the stone marking the grave of a young man "who was cut off by the hand of a wise but mysterious Providence in the twenty-third year of his age, the week before his expected nuptial." One can only wonder how "wise" the bride-to-be actually found the hand of Providence to be.
Historians estimate that there were as many as 4,000 people buried on the site when it took up a city block & located, perhaps not coincidentally, across the street from that other repository of stiffs, the Duquesne Club, and beneath the office building that houses the Allegheny Conference on Community Development. The problem was that, in a rapidly growing metropolis, the living were crowding out the dead, especially in the centrally located Golden Triangle. There was too much demand for new offices, new warehouses, even new mausoleums like the Downtown Lazarus.
The question, of course, is the same question that plagues many decisions pertaining to developing Downtown Pittsburgh: Where do we hide the bodies? And as you've noted, in the 1840s, the solution presented itself: Allegheny Cemetery, one of the country's oldest rural-styled graveyards, opened for business, and the Trinity burying ground gave up all but an elite handful of its dead.
Such moves were not uncommon during the city's growth: One Troy Hill cemetery, for example, was populated with bodies which were moved from Smithfield Street in 1860, and then relocated to Homewood Cemetery 30 years later. And who knows? With population trends the way they are, maybe the process will reverse itself, and living people will have to clear out to make room for the corpses.
To watch a Pirates relief effort, in fact, is to suspect it's already happening.