This does a lot of that for the client: https://github.com/jgstew/tools/blob/master/bash/install_bigfix.sh
It doesn’t take much more to make it a relay from there, especially if your relays follow a naming convention, then a policy action could do it for you.
I’m really talking about making relays easier, not using a Tiny Core Relay specifically.
I run the BigFix Client in a docker container for testing using the script above. It should be possible to run a BigFix relay in a docker container as well, though I haven’t tried it.
Now that I have read over the TCL relay instructions, automating a relay on docker seems easier.