The only King's Heirs that are specifically recorded are those of Tar-Elendil, Tar-Meneldur and Tar-Aldarion, the fifth, sixth and seventh Kings of Númenor respectively. We know that announcing an Heir was already a tradition at this time, but we cannot be sure when that tradition started, nor how long it continued after Tar-Aldarion's time.
The earliest possible King's Heir would have been Vardamir Nólimon, the son of Elros Tar-Minyatur the first King. Since the Heirship was traditionally bestowed at the age of one hundred, for Vardamir this would have been in the year II 161. In the event Vardamir immediately resigned the Sceptre to his own son Tar-Amandil, which casts some doubt on Vardamir's own status as an official Heir. Indeed, his precipitous abdication may have been the original reason that future Kings would announce a formal King's Heir.
The last King of Númenor, Ar-Pharazôn, had no offspring, so the last possible King's Heir would have been that of his predecessor Tar-Palantir. This would have been his daughter Tar-Míriel, who would have reached her hundredth year in II 3217. It is unclear whether she was ever officially designated King's Heir, but she was at least legally entitled to the position (though in the event of her father's death, the throne was in fact usurped by Ar-Pharazôn).