Both Scotch and Irish moss will not flourish in shade. They are not mosses at all and need a lot of sun and a relatively rich, fast draining but moisture retentive soil.

True mosses shouldn't be all that hard to encourage. If you can harvest some from a woody area, mix it with buttermilk or yogurt in a blender (not one you will use in the kitchen afterwards :-)), spread it on the area you wish to culitvate and keep damp. The moss will rapidly colonize this spot as long as even moisture in the area is maintained - if the soil is allowed to dry out, the moss will die.

If you can grow them, Selaginellas or the spike mosses, are a good substitute. Also not true mosses but liking the same shady, moist conditions as the true mosses. Most are not very hardy, though, preferring higher climate zones.

Not exactly mosslike, but sedum acre is a low growing, nicely spreading ground cover for shade. It blooms bright yellow, tiny flowers in the spring and is evergreen. If it breaks when you step on it - no problem - new plants!