Saraswati seems to be the most well known. A Hindu/Vedic/Buddhist deity of knowledge, learning and the arts, she is often regarded as a patron goddess of both literature and scholars.
I came across an interesting fact while researching her – traditionally, Hindus believe that books and texts are sacred to Saraswati, and to place one on the ground and/or touch one with your foot is considered blasphemous. If this is done accidentally, the book is then touched by the forehead (the site of knowledge) to counteract the offence. I just love the idea of books being seen as sacred – like most book lovers, I’m incredibly passionate about mine!
Another ancient goddess of writing, who I personally haven’t come across before, is the Egyptian Seshat. Part of the older pantheon of Egyptian deities, she was later co-opted by god of learning Thoth – and demoted to being his daughter – but she was originally credited with the invention of the written world and was also the patroness of libraries and historical records. Her name means ‘she who scribes’.
Although my research didn’t uncover any goddesses specifically for romance writing, I did find the Greek Muses, one of whom, Erato, is the muse of love poetry.