Are you zoned R-1, single family residential? I guess if the funeral director is in negotiations, he probably already knows the answer. A sale could hinge on a zoning change, and you would have a good argument on it changing the character of the neighborhood, possibility of hazardous contamination (from chemicals) and certainly traffic....residential streets are not generally designed to handle the load of traffic a funeral brings. A funeral home would need a large parking lot which can equal water runoff which your sewer system may or may not be able to handle. If it comes to a zoning hearing, I have some ideas of things which can be brought onto the table.
If the street is wide, the houses wide spread, it honestly wouldn't be the worst neighbor. The elderly man may think he has no other option, but if he hasn't talked to a real estate agent, he might be surprised at what price he could get from a buyer. You recently moved there, so people are coming into the neighborhood. I bet you can get someone into the house and not in a coffin.
If the street is wide, the houses wide spread, it honestly wouldn't be the worst neighbor. The elderly man may think he has no other option, but if he hasn't talked to a real estate agent, he might be surprised at what price he could get from a buyer. You recently moved there, so people are coming into the neighborhood. I bet you can get someone into the house and not in a coffin.