Here's the command:
#!/usr/bin/env bash
docker run --rm \
--workdir /app \
--volume ${PWD}:/app \
--volume ~/.ssh:/root/.ssh \
--volume ~/.composer:/root/.composer \
composer/composer:php5-alpine install -o -n --no-scripts --ignore-platform-reqs
This is the (eventual) error:
error: cannot run ssh: No such file or directory
fatal: unable to fork
It seems like alpine is missing ssh, using the non-alpine version solved this problem.