You can make a general search using Google like this:
"I suppose not" = 255.000
"I don't suppose so" = 793
then you can make a restricted but more reliable search like this:
"I suppose not" site:nytimes.com = 22
"I don't suppose so" site:nytimes.com = 0
This search generally does not indicate grammatical correctness or incorrectness, but gives an idea about the frequency of the phrase.
Now you know that "I suppose not" is used more than "I don't suppose so".