I live in a apartment as well, all though I get amazing sun exposure since I'm high enough off the ground to avoid the shade of near by trees. As long as you get at least 4 hours a day direct sun, you should be able to get some peppers to fruit.
Anyways, I grow scotch bonnets, Jamaican red hots, super chilis, and am trying to get the super hots to fruit this year. I purposely limit my pot size to about 5 gallon so I can grow more varieties, but obviously this effects the yield. Personally I care more about having 8 or 9 different types of plants than 3 or 4 monsters.