Here is my suggestion for never. The words comes from "ever" + n negative. "ever" would translate "永" (eternal, always). I'm not sure which negative kanji suits best 無　非　否.
Here is what my kanji dictionary says :
否 : say no, deny, is not, or not
非 : is not, not, non-, un-, in-
無 : without, nothing, -less, non-, un-, in-

Still difficult to choose. I like feeling of 否 for the idea that you don't want to do sth. or will not do something, but 無 is maybe more natural in this kind of compound (in Japanese at least).

So, I propose that 永's reading be "ever" alone, 否永 or 無永 be used for "never". We still need to find other compound for "always/forever/everytime/all the time" and "eternal". I thought of 永時 (eternal time) for eternal. Every or each is "毎" in kanji. The problem is that in English "every" comes from "ever" (though there is no such relationship in other European languages) Everytime could be either 毎度 or 毎回. We don't want to reduce 4 words into one kanji neither, so each of them should have a different one keeping the nuance. Forever has ever in it, so will use 永. "Always", "all the time" and "everytime" won't. What's the kanji for "for" ?

I have come to realise that European used much more preposition in compound words that Asian ones. Just take "preposition", postposition", "composition", "repositioning", etc. It would be easy to put into kanji if there were suitable kanji. pre-(前), post- (後) and re- (再) evident, but some like com-, pro- or for- aren't. Interestingly, these suffix are explained in Japanese in my electronic dictionary - probably because it helps Japanese people guessing the meaning as they are used to kanji. This motivates me even more to transcribe English into kanji. Does anyone know Chinese kanji on this forum ? There must be kanji for preposition in Chinese.

To be continued...