Hi there,
 
The only real way to get a cherry jam or jelly to set is to add a pectin to
the mixture especially if you are using honey.  Choose a recipe which uses
either liquid or powdered pectin as this helps the jam or jelly to set (some
recipes use agar-agar) and then you will have to adjust the water content to
replace sugar with honey.  It is quite complicated and a matter of trial and
error.
 
I have played about with a number of recipes but am not familiar with your
type of cherries.  I will have a look and see if I have a more specific
recipe but roughly if you replace the sugar with  three-quarters the amount
of honey that is reduce the quantity by a quarter and reduce the liquid
content by a fifth it should work.
 
Also I have now looked in a copy of 'Putting it up with Honey' by Susan
Geiskopf on page 50 there is a recipe for Blackberry Jam with suggestions
that you may also use chokecherries instead.  If you need further
information on this please contact me direct.
 
Barbara Dalby, author of many honey cookery articles.