the regional trains from Trèves to Coblence do have bicycle facilities and some of the wagons, but the train is during spring and summer quite charged with bicycles.and the places are limited. There is a high risk on week-ends with good weather conditions, that there is not enough place for your group because there are many people using this train going back from a bicycle trip. I suggest to contact in advance the exploitant, the CFL ( chemins de fer luxembourgeois), to make a reservation for a group (I do not know if this is possible, but give it a try).
You can try do this also at a German train station with a guichet of the Deutsche Bahn, but this regional train line is run by the CFL.
all the best