Merriam-Webster says that the adverb form of "supposed" is indeed "supposedly," but the adverb form of "supposable" is "supposably."
Webster's New World is a little vaguer, noting "supposably" only as a "related form" of supposed. However, because WNW has a separate listing for "supposedly" and none for "supposably," there's no doubt which form they prefer.
So, what, exactly is the difference between the adverb form of "supposable" and the adverb form of "supposed"? In their adjective forms, they're clearly different. But as sentence adverbs, the distinction blurs.
I'm going to have to think on this one for a long, long time (after I stop retching, of course). Until then, I'll file this under "things I should have looked up a long time ago."