The smallest 12V lead acid battery I've got is roughly 10cm x 4cm x 5cm. It's rated at 1.3Ah so it should be capable of powering the display for several hours at least if it only needs 90mA. You can get bigger sizes and it'll last longer.
Hooking it up with a trickle charger should keep the battery topped up. You'll need to put a diode in to prevent the battery discharging through the charger.