Unfortunately no, you can't mount a window air conditioner in a sideways orientation on the ceiling.
The best setup for a cooler with no outside walls is a ductless mini-split air conditioner. The evaporator hangs on the wall in the cooler, the compressor sits on the ground outside, and the two are attached only by tubes and wires so you only need to make about a 3" hole in your cooler.
Venting the A/C into an air conditioned space is an option, but you will be paying for the additional electricity to cool the warm air blowing into the air conditioned space.
Portable air conditioners are not a good option since they are unlikely to get your cooler below 50F (even in the best of circumstances.