Don't know where you are, but the first thing I'd do is find where the old passenger rail stations were in the county and figure out which had trains running to New York(where most orphan trains were from) or Chicago(where NY trains connected to West-bound trains) depending on which part of the country you're in.

As WYSIWYG pointed out, rail buffs of one sort or another are going to be the ones who know about this.

Next, I'd check the newspaper archives of those town/cities for articles, because the arrival of an orphan train would have been well publicized, keeping in mind that the phrase "Orphan Train" is a term of convenience that has been attached to the effort over time, rather than the actual name of the effort.

Another thing to keep in mind is that this is one of those things like Japanese Internment Camps, The Trail of Tears, and Involuntary Sterilization--that is to say, not one of our better moments, so you'll have to dig for information--

Good luck with this!