Regional location? Soil conditions? Gardening habits (of friends) - are they likely to water etc.?

It depends on how small is "small", but you shouldn't be too limited in choices with regards to light conditions. A 6' fence (pretty typical height and widely used throughout many gardens) is not going to limit much sunlight - it's simply not tall enough to provide much blockage.......just at specific times of day. If on direct compass layout, the interior of the eastern side will be shaded in early morning, the western side in late afternoon, but the southern face will receive a great deal of sunlight in all but the deepest part of winter when the sun is lowest on the horizon. Shrubs, vines and perennials that are suited for sun to part shade should all work.

You may be more limited by planting space. Are there beds in place now? If so, how deep? Most gardens seem to have perimeter planting beds that are of minimal depth - 2-3 feet - which won't accomodate much layered plantings to provide a full, lush appearance. If possible, increasing the beds to a minimum of 5-6 feet will offer greater opportunities for diversified plantings that will provide greater visual interest. And of course, you want to vary choices as to flowering times, foliage color and texture and offer a variety of heights and growth habits as well. But light conditions are unlikely to be the overriding concern you imagine.

Thanks a lot. The amount of sun was my main concern so anything that does well in partial shade should work. There are no plants at all now - just grass. It looks pretty bleak so anything will be an improvement. Just depends on the budget.

I wouldn't plant anything in the ground in a small back yard rental. It's way easier and more appealing to me to buy tall evergreens that do well in pots, like golden bamboo, black bamboo, or even bargain tall Emarald Green Arborvitaes's.
Your friends can take them when they leave.