What is a good dwarf conifer for shady area?
In general terms, firs (genus Abies), yews (Taxus), hemlock (Tsuga) and arborvitae (Thuja) are all relatively shade tolerant. Most cedars (Cedrus), spruce (Picea), pines (Pinus) and junipers (Juniperus) are not.
For full shade, yews and plum-yews (Cephalotaxus harringtonia) and hemlock are best, although hemlocks should generally be avoided as they are susceptible to the woolly adelgid pest. Nevertheless, the NYBG's Benenson Ornamental Conifer Collection (BOC) has a nice specimen of Tsuga canadensis ''Jervis' which is growing well. Also, a variety called 'Gentsch White" is relatively resistant to the insect. If you decide to plant a hemlock, talk to the nursery you buy your specimen from about ways to protect it from the woolly adelgid in your area.
For partial shade, the BOC has an American arborvitae with blue foliage (Chamaecyparis obtusa 'Split Rock'), a bright gold arborvitae (Chamaecyparis obtusa 'Tsatsumi Gold'), a dwarf Serbian spruce (Picea omorika 'Nana') and a spreading Greek fir (Abies cephalonica 'Meyer's Dwarf').
If you want a "Christmas tree" shape, then a fir is probably your best choice. The U.S. National Arboretum has a useful web page on the "Dark Side" of conifers:http://www.usna.usda.gov/Gardens/faqs/darkside.html
Also, the following website has a nice list of conifers suitable for growing in the shade, and it lists the final height of the trees, which is useful:
You have a little time to Google images of all these trees and make your choice, as most conifers should be planted in the late winter or early spring.
Hope this helps.