When in doubt, just reword the sentence:
A corporation may not have a conscience, but it does have a PR department.
Corporations have PR Departments, and if you don't have a conscience, a PR department will do.
No corporation has a conscience. But all of them have PR departments.
Of the options you proposed, the one that sounds best to my ear (as a native speaker of American-English) is the second: Corporations may not have consciences, but they do have PR departments.
The clause "corporations may not have a conscience" implies one conscience shared across all corporations, which seems wrong. Each corporation would have its own conscience, just as each corporation would have its own PR department.
On the other hand, the following does sound right to my hear: Corporations may not answer to a god, but they do have PR departments. This implies one god shared across all corporations, which makes better sense.