I have to thank Madeleine Robins for pointing out that the carriages in French and Belgium at this point were called dilligence. By the way, if you have not read her truly excellent The Sarah Tolerance Mysteries
And now, here is how the dilligence appears in Glamour in Glass
Despite the charming name of France’s national system of carriages, the dilligence was too crowded for comfort, and the views out the windows— though of unfamiliar scenery— were only glimpsed by twisting one’s neck. The dilligence exchanged passengers at inns, crossings, and stables so that they had an unending variety of new travel companions.
Diligence, with one “l”; never two. As in the original word in French, and as borrowed by English, meaning a kind of carriage.
Funnily enough, we were just having that discussion. I have two period sources which spell it with the double L. We were having the discussion about if we should modernize it.