There is service to Coburn from Frankfurt Airport:

Cost $47 Euro (Approx) Duration: About 4 Hours

Go to this URL:

http://reiseauskunft.bahn.de/bin/query.exe/e

and enter Frankfurt Airport and Coburn, dates of travel, and times you wish to travel. A schedule will display with fares (most of the time). Click on "Show Details" for selection, then "Show Intermediate Stops" if you want to see the detailed schedule. Looks like you'll have to change trains in Wurzburg and Bamberg.

Good luck...