@DavidGaughran asks on behalf of friend Silvina De Vita who's recently published her first digital children's book,
In the most basic terms, marketing is about the "4Ps" -- product, price, placement, promotion. The author in question has already determined the first two and possibly part of the third P; she's decided on a children's book (product) to be sold at a set price, with placement partially determined as Amazon.com.
I say partially as the author may decide to move to more or different download venues over time. Price, too, may be flexible over time as more copies are sold.
David's question is really about the fourth P -- promotion. Where does one promote a book for children?
Go where the parents are. And go where mothers are as they will make most buying decisions.
But the product is a digital product; outreach to a completely different constituency is necessary as these will be wired women who are comfortable with purchases of digital products over the internet. Where do these parents hang out?
If I were promoting this book, I'd start with immersion in the BlogHer community. I'd go so far as to consider blogging about the process of writing the book, the decision making process about self-publishing and going digital, asking that community for their feedback about the best approach to marketing. Make a commitment to that community by purchasing ad space from the BlogHer site. It's important that the author embraces the opportunity to communicate directly with her target audience; if she opens herself up to feedback, she must acknowledge hearing from her constituency or risk credibility.
I'd also encourage the author to read Pew Internet & American Life Project studies to identify where the digital parents are and how to reach them. Chances are very good that their research will provide insights about families' internet consumption which will shape promotional outreach.
Parents increasingly use social media to find content they want, and to filter out content they don't want. It's a time saver. What social media do wired parents use? The most obvious resources are Facebook and Twitter. The author should ensure that her book has a dedicated Facebook page, that she has one as an author, and that both the book and the author have Twitter accounts. The author should commit to sending out at least one update a day via each of the social media outlets she chooses, and make a point of connecting with people who are connectors in the target demographic. Is there a parent in the BlogHer community who blogs about children's books? Find them, friend them and follow them and be sure to engage authentically with them.
This is a lot to tackle all at once, but this is an essential difference between the traditional brick-and-mortar print publication process and digital self-publishing. The author will do a lot of work themselves, but they will have more control of their product and personal brand, and they will have a more authentic relationship with their audience.
Caveat here: I'm not a published author. I am, however, familiar with using social media to promote online content -- and I'm a mom who's bought a small fortune in books over more than 25 years.
Good luck! Buena Suerte!