Moom actually does work with Day One, but in a slightly off-target way. That is, in order to get Moom's pop-up panel to show, you have to hover just above the onscreen green button, as seen in the below screenshot:

As long as you hover as shown in the screenshot, Moom's panel will appear. Day One is aware of the issue, and hopes to have it fixed in a future update.

That screenshot is from Peter's Mac—he's the German half, and founder/programmer for, the international two-person organization that is Many Tricks.