The fitting translation for proportion is Anteil in this case, see e.g. Linguee.
I don't think that there are established special terms for "count proportion" and "continuous proportion" in German.
Something that is used is the term zahlenmäßiger Anteil, in the sense of: you have a crate full of apples and oranges, and you can count fruits to get the zahlenmäßiger Anteil of apples, or you can weigh them or measure their volume to get the Gewichtsanteil or Volumenanteil. IMHO this might be a good fit for "count proportion", too.
A different way to approach this would be to look at the terms that are used for variables in general in statistics, which leads to diskrete vs. stetige (or: kontinuierliche) Merkmale/Variablen:
An explanation can be found e.g. here or in any basic statistics text.
Transfering this to proportions, the terms would translate to diskreter Anteil and stetiger Anteil. You can definitely use these and they make sense. Conceptually, the term diskret (discrete) is quite far away from count though.