I would think a doctors office gets a lot of activity, as people are always getting sick/injured whether the stage coach stopped there or not. If you know where the cistern is, you should have an approximate location of the house as they were normally connected.
Do you have a local Library or historical society? Go there next and see if someone can help you find the doctor and subsequent owners. Also ask if they have more information on the stagecoach route. I wouldn't be surprised if you have someone associated with the historical society who is very knowledgeable about the stage routes. There may have even be a book on the subject by local people in your area. Someone may also know where the stagecoach stops would have been, so that you try and get permission to hunt those properties too.
The historical society also may have old pictures of the property and old maps not available online.
**Edit - I was looking after I posted this and found some quality maps**
I was just looking and you should go to USGS Topo Viewer and search "Livingston, AL".
USGS Topo Maps Online Viewer
There are some good early (1:65000 scale) topo maps from 1932 and one earlier (1:48000) one from 1928. Hopefully your property shows up on those. If not, they probably exist but you need to search a town that is on the next grid square.
I would recommend you download Google Earth, and then download the topo maps KMZ files. From Google Earth, open the map KMZ file you downloaded and it will overlay onto Google Earth. From there you can use sliders and layers to move between views.
Here is a good tutorial showing how to do it.
Open USGS Maps in Google Earth Tutorial
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