I have experimented with other exercises, but journaling is my primary Stoic exercise, although I journal a variety of ways.
One of the better starting points (not historically Stoic, but influenced by Stoicism) is the philosophical meditation routine from the The Philosopher's Mail, although I personally bring more Stoic elements into it by, in addition to the questions listed there, I ask what the different experiences say about what I value, whether these values concern virtues/vices or externals, and what virtues and vices do apply.
Although I think it clear that writing was an important element in ancient Stoic training, explicit instructions are lacking. The best references I know of are Marcus Aurelius's Meditations as an example of such writing, Epictetus's Discourses I.1 and II.1. There is also Seneca's letter 84.
Other journaling ideas, some Stoic (or at least related to Stoicism), some not (repeated from an [earlier comm