Well, I would say... Sometimes the answer is so easy that one does not even consider it?
Especially since this poem was made only after the Rings have been already distributed (and probably for a long time), this obviously means plainly their original three owners, or their bearers at the time of making of the poem (I don't think there is any evidence as to when exactly it has been made, but definitely "old"). Since three are mentioned, it must have been Gil-Galad, Galadriel and Círdan; possibly even with Elrond instead of Gil-Galad, if the verse is of later date and spoke about the contemporary bearers.
It certainly does not mean that the Rings would be "made to be given" to any Kings, it just means that "Three Elves have Three Rings, Seven Dwarves have Seven..." etc.
There certainly have not been any "kings" (except for Gil-Galad) in the literal sense of the word, but they were all powerful rulers of the Elves, and technically speaking, they were kings (and a queen).
(edit: crossposted with Mith)