There is a national organization called Rails to Trails, that rehabilitates former railroad track sites into suitable hiking trails. You can find them online with a simple search. There you can find info on suitable and available trails.
There are a number of excursion type trains run by clubs or for profit entities. Best bet is to have an idea of where you want to camp, then locate org.'s in that area and contact them as to possibility of doing what you suggest.
By the way, I have found that there are many high adventure camps in the Mid-Atlantic and SE that are in close proximity to these type of scenic train excursions. Smoky Mtn RR, TN Valley RR, Blue Riidge Scenic RR, just to name a few . . . I would be interested in hearing how it goes.