The Court of Appeal dismissed the appeal, saying it was not an element that needed to be proven beyond reasonable doubt.
Milner appealed to the Supreme Court on the ground that the verdicts were unsafe unless the Crown could prove beyond reasonable doubt how the drug was administered.
The Supreme Court upheld the Court of Appeal's view that the method of administering the drug did not need to need to be proven. It was enough that the judge directed the jury to be sure that Milner had drugged Mr Nisbet without his knowledge.
However, during the appeal process a pathologist had contacted Milner with doubts that promethazine was the cause of death.
Mr Nisbet's sister Lee-Anne Cartier was pleased Milner's appeal was rejected.
"We can finally close this chapter of our lives," she said.
However, she added: "It's just a shame that the so-called justice system allows these fruitless appeals to even be considered."
The Court was asked to grant leave to appeal on the basis that the new evidence would have raised a reasonable doubt if put before the jury.
But the Court said the expert opinion was tentative and did no more than raise lines of inquiry into other explanations for the death.
Should more evidence emerge, an application for leave to appeal could be considered.