When we needed some feather-edge coach bolts for the wings of the fire engine one of the club members (a famous loony) re-machined metric bolts. He used MNC, Manual Numeric Control, for the heads. He had a table of coordinates and dialled them in by hand on the lathe handles.
M16 is 10/16" so I would imagine that you could find some 9/16 coach bolts hiding inside metric 16mm ones.
M14 is slightly undersize for 9/16. And I rather expect that M14 coach bolts are rarer than 9/16.
However M16 coach bolts are likely to be 2mm pitch, so I imagine that you would need to cut all the thread off of over-length ones to get a good thread.
Alternatively, perhaps try the US, but again buying over-length and re-threading.
https://www.fastenersclearinghouse.com/fastener-search=carriage-bolts&size=9/16-12&Cat1=PRM460D65E02814;&Cat2=FL3DCA0E45011;