A friend of mine (who lives in the European Union) wants to rent a car
somewhere near Coffs Harbour in New South Wales, Australia
(http://www.visitcoffsharbour.com) but the problem is that he's 19
years old and all greater car hire companies in Australia demand a
minimum age of 21. He got his driving license more than one year ago.
Is there some smaller company which rents out cars to people at age
19?

It is virtually impossible to rent a car in Australia if you are under
21. This age limit is set by all the insurance companies. If he is
staying for a little longer he can just purchase a cheap car that will
do the job for as little as $500AUD  and comprehensive insurance for
about $25 a month. Tourists do it all the time and sell or dump them
when they leave.

Well, it's not near Coffs Harbour (but it's a nice drive down the
coast to Coffs), and apparently they have charges which you need to
enquire about over the phone, but at least they claim to rent to
people under 21:
http://www.goldcoastcarhire.com/

I hope this helps a little.