Here is my Flyer coupler I that ground down to fit into my 392E. The switch can be done in seconds. Going from a Piper to a Lionel car is another animal. The coupler on the Piper is attached to the center of the truck. You will need the opposite Flyer coupler, the opening end. It would then need to be ground down to fit into the pocket of the first coal car. The Lionel coupler unscrews off and the modified Flyer coupler can be screwed right in. This is reversible in seconds and does no damage to either the coal car or the engine. Cost under $10.
I imagine your Flyer engine is setup the same as the Piper.