Penultimate, heretofore my favorite note-taking app. The sensible thing seemed to be to send a feature request to the developers of Penulimate for an inverse, "night mode." That request met with an unconvincing "great idea!" sort of response, so I went with plan B. I tried unsuccessfully to create a black background custom page for Penultimate. Lucky for me a CFI candidate recently showed me Notability, an iPad app that has a few more features and easily solves the night mode issue.
There is a global night mode available in iOS under Settings->General->Assessibility which inverts the iPad screen colors when you tripple click on the Home key, but doing this has the unfortunate side effect of making aviation charts look odd.
And lucky for you and me, Notability is currently on sale for just $0.99. Check it out!