I've made a web app which should be perfect for this jam, jspaint.app
It's a clone of classic MS Paint from Windows 98, with some extra features.
You can enable transparency by going into Image > Attributes, selecting Transparent, and hitting Okay. Then you can use the Eraser to create a transparent area, and use the eyedropper to select transparent as a color and use the fill tool to replace the rest of the background. Or if it's a new image you can use Image > Clear image, or Ctrl+A + Delete.
More info on the readme.