I hear “supposably” with increasing frequency when “supposedly” is the correct adverb.

Problem:
The adverbs “supposedly” and “supposably” are not synonyms.

Explanation:
The adverb “supposedly” means reputed or believed to be the case; purportedly.

The adverb “supposably” should be used only in the context of capable of being supposed, and this adverb is valid only in American English.

In a sense, most people who use “supposably” are lucky in that it is a “real word” (in American English). But these same people misuse “supposably” as a synonym for “supposedly” (which it is not!).

As I mentioned several days ago, here is an unorthodox but still fairly reliable method to determine which of “supposedly” or “supposably” is more likely to be the correct form: search Google separately for each of “supposedly” and “supposably”; the one with the dominant number of hits or matches is very likely the correct form (unless the language has fallen apart on the Web!).

For example, I just searched Google for “supposedly” and got about 2,770,000 matches; I searched for “supposably” and got about 66,200 matches. This nearly 42:1 dominance of “supposedly” over “supposably” is a very good indicator that “supposedly” is the correct form — at least, in most situations.

I believe that the misuse of “supposably” as a synonym for “supposedly” — especially in speech — is consistent with my “Devolution toward Simpler” hypothesis. It’s simpler to say “supposably” than to say “supposedly” because the first adverb’s ending is simpler to say than is the second adverb’s ending.

Solution:
Use “supposedly” when “purportedly” makes sense as a replacement adverb; use “supposably” only with an American English-speaking audience and only when the intended meaning is “capable of being supposed”.