Can non-EEA parents of a minor Irish national obtain an EEA family permit before travelling to the UK under the new EEA Regulations(UK)?

Persons born in a British Overseas Territory after 21 May 2002 automatically acquire British citizenship (even if they do not acquire BOTC) so long as one parent is a British citizen, settled in the UK, or settled in an Overseas Territory (other than the Sovereign Base Areas).

I would like to know which EU countries are fast to issue a resident card for the family member of EU national. If you know that ,please let me know it.