You've probably already thought of this, but most English speakers (whether Irish or not) are going to see Kyna and pronounce the first syllable to rhyme with "eye" (as in "Kyle").

You can't take much from baby name sites and books...they make shit up with distressing regularity.

Redwolf

Thank you, Redwolf. I am aware of the dubious nature of name websites and books. That's why I'm here. It took me weeks to find this site and I've been asking everyone I know who might be knowledgeable enough to help in this case. This site has been very helpful!

Yes, I'm also aware some people might pronounce it differently. It was a consideration, but I'm fine with it. The alternate spelling is with an "i"—though that is also likely to be pronounced as a short "i" instead of an "ee" pronunciation (important, because it coincides with Kynari being Japanese, which doesn't have short vowels). But I definitely prefer the "y"—with "ee" or "ey" being way down the list with this particular name. But, as someone whose names (first, middle, and last) have been constantly mispronounced all my life, and someone who has lived in multiple countries and seen pronunciation change and change, I don't really see that as a problem. As long as it's pronounceable and not too contrived, it's okay.

I looked cíoná up but didn't find much. Does it have meaning anyone's familiar with?

If anyone else has comments or answers to the questions posted here, I would be grateful for for your post—even if it's just to concur with earlier comments.

Kyna is not Irish. There is no K in Irish either.

Anglicisations and mixing languages does a disservice to both language.
I would give the child an Irish and a Japanese name.
If you want the name to have a K sound then Ciara, Caoimhe, are common choices.
Or Cionnadh, as previously suggested, even though it's not normally a girl's name there is no reason it can't be.

I'd say the child's well named by this stage, a Bhríd.