Is it a blog? You can submit to Free Traffic System to get free content. At the same time, add article to Free Traffic System for the purpose of getting backlinks
Social media will be the fastest route by far, but don't forget a healthy link building campaign too.
If you are having trouble finding time to promote it, guest blogging is always an option to help with content and links. Getting bloggers to create relevant content to promote themselves and your blog will help to keep the website fresh and earning.