I wonder if you can melt Delrin without changing its properties. If it is possible then melting some into a brass eyelet would seem like an easy thing to do. That might be easier than trying to turn down a Delrin rod to fit the eyelet. Maybe even just softening it and mushing it into the eyelet would work.
There are many tools out there that could shape a conical hole – countersink, pointy router bit come to mind. If I were more set up for it, I would play around with some of these ideas.
The coupling thing is a big issue though. I have found that a knuckle coupler on a Flyer gondola won’t close without help. That’s why I have opted for link and/or Kadee couplers (a strange mix, I know). I like to be able to couple cars together without derailing the train.