Some time ago I created an item that would have been a prototype Celebrimbor made before the Three Rings. The Ring of Springtime. The Three all end in -ya with the element before it. Tuilë means spring, springtime. How would Tuilë+ya work?
I would analyse the attested three ring names as formed directly from the roots. Nenya and Narya could also arise from the later words nén, nár, but Vilya, I think, can only plausibly come from √WIL (unless you assume that, unlike the others, Vilya is simply the common noun vilya without further changes).
Nenya < √NEN+ja
Narya < √NAR+ja
Vilya < √WIL+ja
This presents a problem with tuile, which comes from √TUJ; as far as I know there are no examples of roots ending in [j] deriving words with the -ja suffix. So you can't be perfectly consistent with the ring names here. Furthermore, there's a variety of attested adjectival suffixes that are used in this scenario instead of -ja, and I have no idea which would be likelier to use - this requires more research.
I suppose I could tentatively offer Tuina, meaning something along the lines of "Ring of Sprouting, lit. 'sprouty'".
Well Tuina sounds good. lol "sprouty". Maybe I can search out synonyms.
Virya already means "Fresh" or at least "Young" and matches the rest of the ring's names.
céva means "fresh, new, renewed". Céva+ya?
With √KEW (root of céva) you run into the same problem as before. Maybe Ceura will do, though that is also a word (adj.), "renewed".