Docker daemon doesn’t start on boot on CoreOS

Try searching through dmesg, /var/log/messages and /var/log/syslog whyc is it happening so but there is a workaround:
1) Try running chkconfig newrelic-daemon on
2) If (1) doesn't help, try forcing the start by adding /etc/init.d/newrelic-daemon restart to /etc/rc.local, this should be placed there before any exit statement in /etc/rc.local

1- Which is the best way to do it?

coreos-install doesn't work with offline images. But if you absolutely want it to work offline on some machine, you can run coreos-install on the machine, that has branch.release.core-os.net domain redirected to 127.0.0.1 using /etc/hosts, has nginx running with a config like this to redirect requests to coreos servers to a local file. Nginx must impersonate core-os.net server. Never tried ;) But it may even work ;)

4- What options do I have if I can't use a PXE server?

I think you can use CloneZilla to install CoreOS offline. Again, I never tried it, so it's just a suggestion.