Cloth diapering while living in an apartment can create some challenges, but it is NOT impossible.
Here are some tips that I've found helpful in making cloth diapering and apartment living easier.
I live on the third floor of an apartment complex. I have no deck. So basically, I have no personal outdoor area. Sunning your diapers is really the best way to bleach out pesky stains that didn't come out in the wash, but with no access to private sun space, your diapers can get a bit (what's a good way to put this...) colorful. I've found that if you hose off your poopy diaper and then spray with an enzyme solution before putting it into the diaper pail, you can really prevent a lot of the discoloration.
--A cloth diapering mommy that I recently met said her apartment-living friend used to take her diapers out to the pool area and sun them there!--
Now depending on how brave you are, this may be a good option for you.
Also if you have a friend with a yard that will allow you to bring your diapers over during a play date, you can kill 2 birds with one stone.
**but DON'T stress** stains are purely cosmetic and do not affect the diaper at all!
Again because I have no outdoor space, drying my diapers depends solely on the effectiveness of my dryer. I found that if I loaded the dryer with only diapers, it would take 2-3 cycles to get them fully dried. A cloth-diapering mom from church, who has c.d'erd 3 children, gave me this stunning (while totally common-sensical) advice.
--Do a load of laundry first, then do your diapers (or vice versa), then dry them all together! For some reason, the diapers dry better when being dried with other clothes. Then she said, "and if they need some more time, I almost ALWAYS have another load of clothes I need to wash anyway. I can pick out my diapers and keep them in the dryer until it's time to dry the other load of clothes". BRILLIANT!
Now I never waste energy on drying my cloth diapers. I always do it in conjunction with my other laundry.
Space is very limited in apartment living (at least it is in my apartment). We didn't have space to have a separate changing table to organize all our diapering supplies (because YES with c.d.'ing there are necessary supplies). We used our dresser as the changing space and used stacking racks (that you find in the kitchen supplies section of your Walmart for 5$ a piece. They aren't gorgeous, but they are effective) to put our cloth wipes, diapers and covers--utilizing vertical area and not taking up any more real estate in our room or dresser than necessary.
Hope this helps! If you are a cloth diapering mom, with anymore helpful advice please share, or if you have any questions about cloth diapering, ask away!