There are lots of blogging websites available, pretty much with the same features – I suspect all would serve you equally for an online journal. Here are a couple options:
I haven’t used each, but poked around a little in each one. To get the most out of using a blog for your journals, the best thing you can do is use tags, labels, categories, or whatever system a particular site uses to associate one post with another. All of them will let you search and give you an automatic calendar archive.
Privacy
Although there are benefits to allowing someone else consistent, unfiltered access to a devotional journal, there are some easy ways to keep your Blog private. First and easiest … don’t tell anyone about it! Second, each of the options above allow you to make your journal completely private and unsearchable via search engines. Alternatively, for a level of privacy as well as limited access, each of the sites above have various invite only or password protected options for your blog.
mysoapblog
This particular site is published with Wordpress. The posting is simple, the themes and plugins are bountiful, and the tagging is perfect.