We just got back from a trip with our 65 pound Lab, Pepper. She's very good, but always seemed to be in the way. I have now made a 'subfloor' under the r-pod table that rests on a 2x4, it's 'off-center' so I only used one. On top of this, and resting on two 1X2s and the center bar of the table, I cut a sheet of 'tempered pressed hardboard' in two pieces for the dog to lie on. I'm going to coat it with urethane, or maybe paint, for protection against a wet dog. Coating tempered hardboard is very important according to the internet, unprotected, it turns to mush if soaked through.
She was tempted into the area with dog biscuits and seems to like it. I figure when we're cooking dinner or otherwise active or sleeping at night, she can be under the table and when we're eating, she can rest somewhere else out of the way.