I have simply installed a small "glove compartment" under the deck in a boat which has a high enough deck anterior to the cockpit to accomidate this. This is not an "open" system, (just put down your drink) but is accessible through a hatch. On some calm day, you could just leave off the hatch though I have not used it in this fashion. It is convenient to have a small storage area here that is accessible to the paddler without taking off the spray skirt.
I have not bothered to try and "drain" this compartment but this would not be hard to do. My glove compartment actually extended slightly "through" my foreward bulkhead. That bulkhead is fairly close (not much beyond where my feet end) You could create a tubular drain that extended out to the side of the boat above the waterline. Such things are not too hard to create using latex tubing with a little wax on it to further enhance its "non stick" properties and then fiberglassing over it running the tube up along the bulkhead until it gets to the side.