“Amn’t”. Which I believe is a valid construction in parts of Ireland and Scotland.
There’s an article here which discusses ain’t in more detail than I can. There’s really nothing wrong with it other than it is considered colloquial rather than formal. I think part of the objection is that it seems “lazy,” and isn’t just used as a contraction for “am not,” but also for other types of negation, like “I ain’t got” or other persons: “I ain’t, you ain’t, he ain’t, we ain’t, they ain’t.”
Grammarians have found on the word ain’t because the word ain’t was more commonly used by the poor and the lower class, making the word a “lower class” word, and not one that proper grammarians should use.
The time when you need to contract “am not” is when it’s part of a question. “Am I not a man?” sounds rather stilted. “Ain’t I a man?” is too low-brow (stylistically) for many uses. What works as the middle-of-the-road style is “Aren’t I a man?”
And, as I said before, all three possibilities are good English grammar. How they vary is in level of style or formality.
“Am’nt” isn’t really proper English: I thought it was slang in the same way as “ain’t”. Even that Wikipedia article says it’s not Standard English and suggest it should be merged into the “ain’t” article.
Isn’t the obvious answer to your question that the correct way to shorten “I am not” is “I’m not”? Unless I’m missing something. You don’t use the phrase “am not” unless it’s preceded by I. And why would “ain’t” be seen as a properly grammatical contraction of “am not” anyway? It adds completely unrelated sounds.
I think the reason it was so significant and the reason it’s remembered today is that it wasn’t sophisticated. It was a blunt and simple protest against slavery and the hypocrisy and dehumanization that surrounded it.
I think the word ‘ain’t’ has almost magical properties. You can use it to determine if the person you’re talking to has a stick up their ass. Also, it sometimes fits the rhythm of the sentence better and people know what it means therefore it can be useful. I’m a keepin’ it.