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.
Modern English uses almost no diacritics or accents. Specific words are exceptions to this, like "café", "naïve", etc., although they are often spelt without any accents. There are no marks you can use to indicate pronunciation.
In old texts, such as Latin and Old English, sometimes a macron is used to indicate a long vowel: ī, but this is not something you can just mix into Modern English.
According to the Acçented Rëading Alpħäbet, use a "di-dot" (also known as an "umlaut") over the "i". So if David Garner (above commenter) wanted to spell his first name in a way that helps people pronounce it according to the original Hebrew pronunciation, "dah-VEED", he might spell it Dävïd.
Use CTL-139 to get the di-dotted "i". (I used CTL-132 to get the umlaut over the "a".)
References: Acçented Rëading Alpħäbet at http://www.tysto.com/articles04/q1/20040226ara.shtml, and Alt Codes, Shortcuts, HTML Codes For Special Characters at https://fontmeme.com/alt-codes-shortcuts-html-codes-for-special-characters/
Researcher/Author/Educator Dävïd Móntané