Pins, Pins, Pins (I really need a smilie for that, I say it so much). You can pin the covers on. If the covers are PUL with velcro, just pin the tabs to each other. You can do this even if they do not overlap. Lift one tab a little bit, put the pin through the end. Lift the other tab likewise and put the pin through it. Then close the pin.
(Did I mention my little one is named Houdini?)