Hmm, my cats and dogs share space as well.

It sounds like he chases the cat sometimes, unrelated to the couch? Do you have one room gated off, so the cat has a safe place to escape to?

Also, no matter HOW friendly they become, never trust your dog with your cat outside in the back yard. Once the cat spooks and runs, the dog's instincts will kick in.

My cats are indoor only, but 2 will come out with us in the nice weather; Chestnut likes to sleep under the catnip! But I make sure the dogs aren't anywhere around.

Can you produce a chew toy / raw hide (if you use those) and appease him that way? I know the whining drives me NUTS!

Hope someone has some ideas for you.