Thinking about where I would use the iPad a lot, I came up with a concept. A couple of 2" wide hard plastic straps in a J shape that would fit over the typical recliner arm, connected together about 6" apart. On one, a threaded receiver that a rod can be inserted. The rod could be used with fittings to provide a swing table that could tilt and pivot. Or a mount like the Garmin GPS ball mount modified to hold the iPad. An option would also be to thread a flexible arm into the receiver. I like the Gamin way of holding their Nuvi units and it would be easy to make a solid lower unit tray with shock corded retainers at the top.
The idea is something that can be moved out of the way when you get in and out of the recliner and can hold the iPad while you are on the phone, or doing something else. I looked at adapting something already made, but the only one I could find was for a cup holder.