Southdown babydoll sheep are a popular smaller sheep breed right now, but there are a few others. I personally would keep sheep in groups of two or more, but I am sure solo sheep have been kept contentedly before. In your situation, goats actually sound like a better bet. My understanding is that sheep (the east fresians may be an exception) really have not been bred for extended lactations like some goats and cattle have.
http://www.sheep101.info/201/dairysheep.html talks about what you would have to do for year round milk, that is, either keep two groups of females to breed at different parts of the year and perhaps have to use artificial means to breed in the spring, or freeze the milk. Sheep milk is often viewed as a very seasonal product.
With goats, you have more options. "Maiden milkers"/goats with precocious udders will come into milk without being bred at all and some will stay in milk their entire lives. They are hard to find though, but tend to pop up in heavy dairy breeds or lines, especially Saanens it seems. Breeds like La Manchas are often bred for extended lactations. That is, you can milk a doe for 1 to 4 years before needing to breed her again, so you wouldn't have to breed as often as you would for sheep.
That's just what I've heard though, I don't have either. Try backyardherds for more responses and experience.
ps. Dairy animals are a big commitment because they need to be milked 1-2 times a day, depending on what schedule you have them on. I have heard that some people can sneak off for a weekend if they are doing once a day milking and have a kid/calf/lamb to take over for them.
