The executed Quakers were not buried in a graveyard — they were buried near the gallows on Boston Common. Presumably, burial within the graveyard was also a sign of respect, though Puritan graveyards were not formally consecrated. This also comes up in the case of burials for people who committed suicide. In 1688, an Indian servant named Thomas hanged himself, and the Boston coroner "ordered his burial by the highway with a Stake through his Grave." Earlier the same year, the wife of Samuel Marion had hanged herself, but she was given a graveyard burial after three witnesses testified that she had been insane for some time preceding her death.
From the evidence I have gathered, it seems that executed criminals were not generally buried in graveyards, but there are some exceptions. In 1704, for example, Sewall allowed the family of John Lambert, a convicted pirate, to claim and bury his body in the Kings Chapel burying ground.
By my Order, the diggers of Mm Paiges Tomb Dugg a Grave for Lambert, where he was laid in the Old burying place Friday night about midnight near some of his Relations: Body was given to his Widow. Son and others made suit to me.Even if he was willing to let the family bury the body with some sort of dignity, Sewall did not want them to flaunt their actions. Most funerals took place in the late afternoon, but John Lambert was buried at midnight.
This makes me wonder: was Samuel Sewall — who is famous for repenting his involvement in the Salem witch trials — involved with the burial of Rebecca Nurse? Family legend says that the Nurse family exhumed and re-buried Rebecca's body under cover of night after she was executed for witchcraft in 1692. The circumstances seem similar. Might Sewall have given his blessing to the Nurses as well as the Lamberts? Or might the mercy he showed to the Lamberts have been inspired by his guilt over doing nothing for Rebecca Nurse?