php-fpm is a process manager which supports the USER2 signal, which is used to reload the config file.
From inside the container:
kill -USR2 1
Outside:
docker exec -it <mycontainer> kill -USR2 1
Complete example:
docker run -d --name test123 php:7.1-fpm-alpine
docker exec -it test123 ps aux
docker exec -it test123 kill -USR2 1
docker exec -it test123 ps aux