"Dead Babies" by Lawrence Watt-Evans

First appeared in South From Midnight.  Reprinted by Stephen Jones, John Betancourt, including a Year's Best.

Bill Sellers, the narrator, takes his wife to have her baby.  Their baby died, says Doc Everett, on its cord.  Somehow they died get their child right away, so they want their child's body back.  Bill and his wife insist that the funeral director open the coffin  immediately.  It's empty.  Has the doc been stealing babies?

*Half-spoiler* Doc Everett has been saving dead babies for his sister.  To replace the old ones.  Watt-Evans takes it a couple of more strangenesses beyond that.