That map is really fascinating, Crom. Checking it up with modern maps, the stage coach route was almost exactly as the Chester Road (A 452), but with a lot of different names. You can see how it left the London-Coventry-Birmingham road at Stonebridge (81 miles) and passed through the middle of Castle Brom (75 miles), past Pipe Hall (Pype Hayes Park now) and a place then called Blue Bell, which I would guess was the house later called Berwood. Across the Sutton Road (A 5127), and on to what became New Oscott, with the predecessor of College Road (A 453) clearly shown. After that came the Parson & Clerk, and a slight bend to the right which I don't think was as much as appears on the map.
At first sight I thought the road turned right along what became Thornhill Road to Streetly and Four Oaks, but I don't think that is right, as later on the route passes through places like Stonnall, like Chester Road does today.
I love looking at old maps. You can get so much out of them with a bit of mental effort.
Cheers
Peter