All the date extension can do, is tell you the time and date. However using that information, you can calculate anything that is based on the time and / or date. There are algorithms to calculate moon phases, such as:
http://www.voidware.com/moon_phase.htmIt is well commented, so I don't see why you couldn't create this with Stencyl blocks; it just appears to be very basic math.
Another option would be to find a reliable source of moon phase information on the web, and scrape it using the [visit URL...] block, although this would require an Internet connection. I think the algorithm above would be a better solution.