The first 10-20 years trains and stage coaches can make money, but you need to use them combined. A train (with first locomotive available) will be lucrative with about 40+ passengers (I use a 10 cars train with 60 places). To get 40+ passengers per run from the small villages (250 residence), you need to set up end-to-end stage coach lines from stategic points inside the villages to the railway station. I use often 2 lines with about 3-4 coaches per line. The train may have a frequency of about 8-12 minutes, but no more. Try to use just 1 train between 2 villages. After 3-5 years you will get about 30-50 passengers willing to take the train to the nearby village, which give you a nice profit from the train AND stage coaches.
At least, that is what I found out while trying and re-playing. I don’t see how to get yet more profit to be able to both invest in expansion AND save up for replacement later. That is my challenge for the moment.