How do I add Unix executables to the Parental Controls 'Allowed Apps' whitelist?
You could take the approach suggested here.
Open the terminal, then switch to your child's user account with:
su - [username here].
Go to the bin directory you mentioned above:
cd /Library/Application Support/org.pqrs/Karabiner-Elements/bin
Then, give all users permission to execute all the files in the bin directory:
chmod a+x *