In my application I am using module within the package example called examplemod.
My app:
from example imp
Thank you all for your answers. They pointed me in the right direction though none of them worked as written. I ended up doing the following:
import example.config
example.config.CONSTANT = "Better value"
from example import examplemod
examplemod.do_stuff()
# desired result!
(Also, I'm submitting a patch to the module maintainer to make CONSTANT a configurable option so I don't have to do this but need to install the stock module in the mean time.)