Marketing a children's book has an unusual feature: the reader isn't the buyer. Children don't buy books. Parents, grandparents, teachers, librarians and schools do — and that changes where effort is worth spending.
Who you're actually reaching
Four groups, and they respond to different things.
Parents and family, who buy on recommendation and on what looks appealing.
Teachers, who need the book to connect to something they're already doing.
Librarians, who are professional recommenders with real influence and are generally approachable.
Booksellers, especially independents, who hand-sell.
Most free marketing effort is better aimed at the middle two than at a general audience, because one librarian or teacher reaches many children repeatedly.
School and library visits
The highest-value activity available to a children's author, and it costs nothing but time.
Start local. Your own schools, your own library branch. Offer a reading and a short activity rather than a talk about yourself. Children who meet an author want the book, and they ask for it at home.
Once you've done a few, they compound — librarians talk to each other, and schools book repeat visits.
Libraries beyond the visit
Ask your local branch to stock it. Many will consider a local author, and some have specific processes for it. A book in a library system gets read many times by people who'd never have bought it.
Local media still works here
Local papers, community radio and neighbourhood newsletters are consistently interested in a local author, particularly a children's author. It's a story they want.
Teachers need a hook, not a pitch
If your book connects to something taught — a theme, a season, a topic in the curriculum — say so plainly and make it easy. A one-page set of discussion questions or an activity costs you an hour and makes a teacher's decision simple.
Reviews
Ask for them, specifically and individually. Anyone who read it and liked it, asked directly, by you. Generic requests to an audience produce almost nothing; a direct ask to a specific person works surprisingly often.
Social media, realistically
It sells fewer books than people expect, and it takes more time than people expect.
If you're going to use it, one platform done properly beats four done thinly, and showing the work — process, drafts, a character developing — travels better than posts asking people to buy something.
What's usually not worth it
Paid ads on a small budget, which are generally lost. Mass unsolicited emails to schools, which are ignored and remembered. Book fairs where you pay for a table and sell four copies. And paying for reviews, which is both ineffective and a reputational risk.
The thing that matters more than any of it
Having more than one book. Readers who like one children's book look for another by the same author, and a single title has nothing to convert that interest into.
Marketing a single book hard is less effective than writing the second one — which is unwelcome advice, and is what most working children's authors would tell you.