Mimi, as someone who also has lived in a small space studio apartment where a bed would take up half the living space, we sympathize with your dilemma. We initially turned to a modern, metal frame futon to fold away during the day and use as our bed in the evening. But we can't recommend this setup, since the futon ended up aggravating back problems (sciatica!) because of the insufficient support. For similar reasons, we're not sure about chaise or small sofa seating with fold out beds, since these were only meant as occasional sleepers and not full time beds. Guest beds are great for short term sleep needs, but we're worried they'd only be okay for the hardiest of backs for more than a week or so.
In regards to chaise lounges that double up as beds, there is the Cigar Sofa Bed Chaise from Sofa So Good (shown above). Also, the Modernica Case Study Day Bed with One Arm works well as an occasional place to hit the hay; Modernica used to offer a chaise version, which we can personally recommend since purchasing one a few years back, but then again, we would not recommend it as a full time sleeping solution either. Perhaps if you were to have a Case Study frame fitted with a custom made/sized memory foam or natural foam mattress, balancing size needs with ergonomic comfort.
Perhaps some of our readers have good ideas about some small space sleeping solutions that also provide ample and healthy back support?