Last night, Facebook pushed an update to its Android app that lets users update their cover photo from directly within the app. In the past, but it required you to use the Web site in order to actually change the photo.
To change your cover photo using the Android app, make sure you're running the latest version of the Facebook app. Pull up your own timeline and tap on your cover photo. You can then select "View Photo" or "Change Cover"; of course, we want the latter option. Select your new cover photo from the Gallery, align it and then tap "Use" to upload the photo. Watch the video below for a walk-through of the process:
As for iOS users, well, you're going to have to wait until Facebook gets around to updating the app to bring back the feature. Prior to Facebook, users were able to change their cover photo from an iOS device.