There's actually even a chatroom for it: Stack Exchange Community Blogs
There's a staging ground, similar to Area51, called Blogoverflow.com, where sites can prove they're worthy of maintaining a blog. The idea is that the users of a site self-organize the blog, prove they can get post decent blog-posts with some regularity. Once it becomes self-sufficient, it gets promoted to being the official blog of the site.
Note that while Blogoverflow used to be hosted by Thomas McDonald from Wordpress.SE, it got transferred to Stack Exchange last week. With that the Gaming blog even got their own Jin-style theme:
I'm not 100% sure how other sites will be able to launch their own version, though I'd suggest asking Rebecca in the chatroom and I'm sure things will be arranged. Given that the themes are based on the official site design (don't ask how this would work for beta sites), it 'should' be fairly easy for Jin to stick the site's design on your blog as well.
Super User was a bit special, since its a Trilogy site and the blog is part of our Community Promotion, so we got 'blessed' fairly early on.
Note that the blogs are a community effort, so you have to make it work. This takes some organizational work and you need to convince fellow users to help you write blog posts. Luckily, each site in itself is a gold mine of info to write about, you just need to put in that extra bit of effort to make everything into a coherent story. On the Gaming and SU blogs we use Google Docs to bundle all our ideas and try and divide tasks between editors and it works fairly well.
If you need any help, you can always ask the users who are already helping out on the other blogs!