Running out of entropy in virtualized Linux systems seems to be a common problem (e.g. /dev/random Extremely Slow?, Getting linux to buffer /dev/random). Despite of using a
Alpine Linux may be a better choice for a lightweight docker host. Alpine LXC & docker images are only 5mb (versus 27mb for boot2docker)
I use haveged on Alpine for LXC guests & on Debian for docker guests. It gives enough entropy to generate gpg / ssh keys & openssl certificates in containers. Alpine now has an official docker repo.
Alternatively build a haveged package for Tiny Core - there is a package build system available.