I've been playing with trying to get 9-patch images to work for button backgrounds, namely buttons with rounded corners. Does anyone know if this is possible, and if so what tweaks did you have to do to the image and/or button to get it to work?

I use 9-patch images heavily.  Which component are you using and what field are you setting?  Button? ButtonGroup?  Maybe you can share the 9-patch image file you are using for your source.

You could also create your own button or extension on the button. We created a new button that has a lot more options like: adding an icon, setting alignment and padding for the icon/text, handle colours for (un)focused state, handle fonts and also support 9.patch images for the background or focus state. 
We actually did the same for the input field and you can add as much options as you like of course.