I don't have an answer but I sure have a question. What diacritic or accent is used when the letter i in a christian name (with no vowel either side of it) is supposed to be pronounced ee?
It can't be done. In names, anything goes for pronunciation. What I mean by this is, any English speaker will be familiar with the idea that you can't tell how to pronounce a name from the spelling. The flip side of this is that there are no unambiguous ways to represent the sound of a name through just its orthography. Diacritics and accents are rarely used in English, and there is none that you could use for this purpose. If you did use one, different people would all interpret it in different ways. If you're concerned people will mispronounce a name, you'll need to add a note such as "Nika -- pronounced NEE-kah", or tell them in person.