There's a good chapter about sleeping dinosaurs in HP Tracy Ford's "How to Draw Dinosaurs". In fact, correct me if I'm wrong, the main problems are the pubis and the ribs in the way and the fact that dinosaurs lack lumbar vertebrae and that their back can't twist like a mammal's. So big theropods laying on their side are probably unlikely. Just watch a sleeping bird.
IMHO a good example of a resting theropod painting is HP Todd Marshall's resting _Albertosaurus_:
Friendly - Luc J. "Aspidel" BAILLY.