Which kernel module are you looking for?
Perhaps the module you need is available in one of the existing kernel module extensions or, if not, it is available in 4.9.22-piCore-v7_modules.tar.xz?
To reduce the size of 4.9.22-piCore-v7_modules.tar.xz, untar it somewhere, copy only the modules you need to /usr/local and then make an extension out of them.
To compile your own modules, use the supplied piCore kernel source, "make oldconfig" using the supplied piCore config and then "make modules".