Assuming there has to be a Prince that was Promised, which there doesn't, especially in the show, then the following is what is probably intended.
It is certainly not Stannis, Melisandre admits she was wrong there.
DAVOS: The only way for what? They all died anyway! You told everyone Stannis was the one. You had him believing it, all of them fooled. And you lied.
MELISANDRE: I didn’t lie. I was wrong.
Game of Thrones, Season 6 Episode 10, "The Winds of Winter"
She then believes it is Jon Snow
DAVOS: You serve Jon Snow now?
MELISANDRE: He’s the prince that was promised.
Game of Thrones, Season 6 Episode 4, "Book of the Stranger"
Later on she states that Jon and Dany have a part to play but doesn't state either are the prince/princess that were promised.
MELISANDRE: The Long Night is coming. Only the prince who was promised can bring the dawn.
DAENERYS: The prince who was promised will bring the dawn. I'm afraid I'm not a prince.
MISSANDEI: Your Grace, forgive me, but your translation is not quite accurate. That noun has no gender in High Valyrian, so the proper translation for that prophecy would be the prince or princess who was promised will bring the dawn.
DAENERYS: And you believe this prophecy refers to me?
MELISANDRE: Prophecies are dangerous things. I believe you have a role to play, as does another. The King in the North, Jon Snow.
Game of Thrones, Season 7 Episode 2, "Stormborn"
Note at this point that D&D would have known they wanted Arya to kill the Night King as they stated in the Inside the Episode for Season 8 Episode 3 that they've known she would be the one for about 3 years so this was foreshadowing for her not Dany.
As such I think we can confidently state that with these events and that Arya actually kills the Night King that Arya was the Prince that was Promised.