The negation of never would have to be 'ever' or 'always'. There are also other words you can look up in a thesaurus that are similar to the words suggested above, but those two words suggested above would mean the exact opposite of never. Saying 'not never' would not only be grammatically incorrect but it sounds bad as well
Instead of using a double negative (which is confusing and generally not good English) you can say "always" or "all the time. " Both of these have the opposite meaning from "never. "
There are two common options: you can use either "always" (if you mean the complete polar opposite of never), or "sometimes" to simply negate it, and to indicate that it is "not quite never".
You can say: "not ever", as in "I will not ever do this". You can also say, "This is impossible, I will not consider this in any conditions. " Or state, "not under any conditions, not in any situation. "