Do you mean Falls Church City or the part of Fairfax Co known as Falls Church, or both? Also, what size and type of property are you looking for?
In any case, there are only two listings in Falls Church City that right now are both for sale and for rent. They are both short sale condos in the newly built Byron on Broad St. Since they are short sales, it is pretty unlikely you'd be able to work a rent to own deal.
However, my own personal philosophy would be that if you see a rental property you like, it can't hurt to inquire about rent to own. Some owners have never considered it, some are just waiting for the right tenant, some may be getting tired of being a landlord but haven't had time to put their place on the market, etc etc etc.
You can also approach the situation from the other side. If you see a desirable property that has been on the market for awhile, it might be worthwhile to ask them about rent to own. Perhaps they are getting anxious. Perhaps it is vacant and they are getting tired of paying a mortgage on an empty house. Again, it can't hurt to ask. This approach probably won't work unless it has really been on the market for awhile.