"Annona" is two things: a Roman deity/goddess figure, typically portrayed holding a cornucopia or with a Roman style ship (i.e. a trireme); it is also the scientific name of the sugar apple tree. I'd love to see one of these ideas portrayed in the logo: the sugar apple fruit, a cornucopia, a trireme, the goddess figure, or any or all of them combined. Or surprise me with something else, if you have a better idea.
Whatever the final logo is, it should be able to be embossed on hardcover books and so look good both with and without the name "Annona Press," and should be visually distinct enough to be recognized and not too "busy" or difficult to read/understand when resized to work as a website logo or an imprint on a book.
I would prefer a serif font, but if you can make it work with a sans serif font I'm willing to take a look. Attached are several images: a sugar apple fruit; a coin bearing the "Annona" figure; and a couple of basic attempts at a logo using a trireme, cornucopia, and sugar apple.