I wonder whether something like a bag-o-wine approach could work here. Instead of using a rigid container to store the carbonated beer letting in air as beer leaves, a bag just shrinks with the loss of volume. Has anyone tried this before or know of any products that might suffice here? I'd have to take a look, but I'm pretty sure I have something like this used for storing drinking water while camping. Not sure how it would behave with carbonation, but it should work in theory I'd presume...
You still have to maintain pressure on it to keep carbonation. What you could do is have a pressurized rigid container that contains a bag of liquid. The air pressure on the bag would not allow the dissolved gasses to come out of solution. I believe this has been done before, but it is not very popular.
I'm sure you have opened a can of pop before. If you let it get warm, it will lose carbonation very fast because warm liquids cannot hold dissolved gases. If you keep the can cold in the fridge, it may stay carbonated overnight because cold liquids can hold dissolved gasses better.
However, air pressure can counter these effects. That can of pop is under extreme pressure at room temperature, yet it is still carbonated. The air pressure inside the can is not allowing the carbonate to come out of the pop. If you were to put ice cold pop into a vacuum, the carbonation would come right out of the liquid. Each situation has a level where the dissolved gasses will equalize with the environment
warm liquid/low pressure = no dissolved gasses
warm liquid/high pressure = some to lots of dissolved gasses
cold liquid/low pressure = none to some dissolved gasses
cold liquid/high pressure = lots of dissolved gasses
Be warned that my terminology is not a substitute for numbers and certain situations can yield different results.. but this is just a general idea