Here are some of the social media genres you might consider using:
Blogging. Blogging is the most similar to a diary, although the possibility of comments adds a new element that you can include if you want. If you go with blogging and want to use blogging software instead of Google Sites for your Storybook, please do so! (There are lots of free blogging software options out there: Blogger.com, Tumblr.com, and many more!)
Twitter. Twitter is a form of "microblogging" with its own special writing conventions such as hashtags, retweeting, etc. To include a Twitter dialogue as part of a story, you can use a Twitter generator. I like Fake Tweet Generator, but if you Google "fake Twitter" or "Twitter generator," you can find lots of options.
Facebook. Just as there are fake Twitter generators out there, you can find fake Facebook generators also! (I haven't played around with these since I am not a Facebook user, but I am sure you could find one that you like.)
Pinterest. You could build a Pinterest Board and then use "pins" as part of your story. You can do screenshots of the pins, or you can embed a whole Pinterest board inside your story.
PostSecret. This website is a fascinating combination of public and private, with people taking their most private stories and making them public. To get a sense of how you can work with PostSecret images while adding stories to them, see this Post Secret Sanskrit Storybook.
Meme Generators. There are also some meme generators that could make a good basis for a story. The "What I Do" generator, for example, could provide a fun illustration to go with a blog entry.
Email and Texting. Since email and texting are modern variations on traditional letter-writing style, I've covered those on the letter-writing page.