I completely understand your hesitation to fostering to adopt. BTDT. However, in most states, you can clarify that you'll only take children IF they are completely free and adoptable. (This is what we went to, because the process of having them leave after almost one year, was too much to bear.)
But, if you decide to go the private route, I can assure you that some agencies DO place toddlers. Perhaps not very often, but it happens. If you decide this, Google 'adoption agencies in (whatever your state is)' and a long list of agencies will be available.
Print this list off, and sit down with a phone to start calling them! When you talk with them, ask them how often they place toddlers. You might be surprised with some, and it certainly can't hurt to ask!
Good luck to you....
Sincerely,
Linny