There's no real ligature for those, but those characters don't really take up any unnecessary whitespace. Combining low and high punctuation marks makes more sense. You could try to turn "! into a well-kerned '!', with he quotation marks very close to the exclamation point, but for the question mark such a system would probably not work.
That said, perhaps there's something to be found in other languages. Some quote with «quote», some with “quote”, others with „quote“, and there's many other variations. I can see how ligatures can work with constructions such as ¿question? can have the quotation makes placed closer in the beginning of the question marks, especially with the slow change from the angled brackets to the English quotation marks in some Spanish speaking countries.