"Supposably" sounds awful (to my ear) and I'm surprised at how often I hear it said. How often would it have to be used within the general population for it to become an acceptable alternative pronunciation to the correct word "supposedly"?
This phenomenon happens all the time. What we call "language" is nothing more than the words that people are actually using. When enough people use a word or pronunciation or spelling for a long enough time, it becomes part of the language. How long this takes is hugely variable, and depends largely on how useful people find the new construction to be. Thus, new tech jargon is assimilated very quickly. Other things (like "gaol" becoming "jail") take hundreds of years.
"Supposably" is very far from the point of becoming standard English. The reason that "supposable" sounds so wrong is that you expect the "-able" adjectival ending to be used with transitive verbs--the object of the transitive verb becomes the thing described by the "-able" adjective. Typical usage of "suppose" isn't really transitive, so "supposable" sounds wrong. The first step toward "supposable" becoming accepted is for transitive usage of "suppose" to become common.
Supposably has been a word used in the written record since 1739 according to the OED. Supposedly since 1597. Both have almost the same meaning, 'to presume something is true,' however supposedly means 'to presume truth without evidence'.
Both are considered correct Standard English. Supposably has died out of use recently except in the US, which is why you may think it is an alternative pronunciation.
I suppose (heh heh) that if everyone who heard it thought that the "supposably" distortion of "supposedly" was better, then, like all successful memes, it would become adopted into common usage and become the dominant pronunciation. However, it would have a long battle to get there.
Next, we'll have syllabub replacing syllable.
Supposably and supposedly have different meanings, because their suffixes have different meanings.
-ably means it is possible. -edly means it has been done.
Supposably is not an alternative pronunciation of supposedly. Supposably and supposedly are two different words. It can only be said of a single word that it has alternative pronunciations.
Correct or incorrect isn't relevant. Ultimately the meanings of words will change and become what the majority decide they mean. Consider terrific and horrific, which were initially synonymous along the lines of their root words, terrible and horrible. Unfortunately or fortunately, the English language is a living thing and subject to change without notice by those who use it. Though I abhor the use of words like supposably, I can imagine the day when words like it will be of common usage, irregardless of my opinion. It could be considered ironical.
I used to study linguistics at Paris V, and one day, around 1987 or '88, I was roaming the halls of the Sorbonne and somehow ended up sitting and chatting with Andre Martinet and Jeanne Martinet. If I recall correctly, Martinet maintained that the correctness of a word is purely statistical. If enough people use it, it's a real word. I also studied under lexicologist Robert Gallison, who was one of the people, again if I remember correctly, who decided what words made it into the Larousse. Supposably, in some alternate universe, elephants have wings, and therefore, depending upon whether that universe really or only supposably exists, they do or merely could. And yet, I wouldn't be caught dead using the word "supposably" in an actual conversation.