Which agency are you looking for? Most apartment communities have their own on-site management. Smaller private owners may or may not (most likely not) use some agent to represent them. As for a listing database, there isn't a major central one, like MLS. Majority of private owners post on Craigslist (watch out for scams, make sure you check the property, their ID, so it matches to the property title, and write checks, not cash). Some, represented by agents may list on MLS, but rarely.
I usually just post my properties on Craigslist, because that alone is enough to keep my phone ringing non-stop for a week.