PDFMaker provides rather good tag management.
Acrobat Pro's feature that provides tags to an untagged PDF is ok for those less complex PDFs.
APIs ? afaik - no.
Also, Acrobat Pro includes a “Make Accessible” action wizard that will walk you through the accessibility steps that Adobe considers necessary - though not “without any manual intervention” - then run the not-very-thorough built-in Accessibility Checker. Whether this will be enough depends on just how accessible you need your document to be. You will never achieve WCAG 2.0 or ISO 14289 (PDF/UA) compliance without some (usually considerable) amount of careful, knowledgeable human inspection of the tag structure and document properties, and associated manual repair action.