There's no need to sound so denigrating Stefan! I am very grateful for Janet's highly respected gift for identifying plants, her sharp eye for minor and differentiating details, her carefulness to come to a final id conclusion for a plant!
And not to forget the enormous time she spend researching for others!
The good-will, interest and knowledge of Dave to help where he can!
We are not light-hearted about finding an ID as proves this thread!

Seeing Myriam's photos and learning new plants is interesting, educational, and entertaining!

Here's some more Hawaiian Rubiaceae:

1st Gardenia remyi

2nd Hedyotis terminalis

3rd Canthium odoratum

I appreciate your zeal and patience all, It's a job for Sisyphus.

Thanks Dave for your interest and posting more of your interesting finds in your corner of the planet!
The Gardenia must smell gorgeous!

Here is a sample of eucalyptus identification
http://www.anbg.gov.au/cpbr/cd...

Psychotria racemosa looks like a match!
I have spend hours on searching, it wouldn't let me lose..
One of your links Janet brought the solution!
The flora do Brasil has two pics of Psychotria racemosa, one shows pointy growths in the leaf axles.
, the other shows the berries which are a match in colour and arrangement.
http://floradobrasil.jbrj.gov....
And then I came across these very excellent photos:
http://sura.ots.ac.cr/local/fl...

I'll make a crop that shows those pointy 'growths' in the axles (what would the botanical term be for that?)

Looks good! Maybe the pointy growths are called spines?

Off to plant my acorns.

Ah 'spines' that sound better, thanks!

I have been looking in my Brazilian plant maps of the year 2013-2014 and found a Psychotria species from which I think is also Psychotria ramosa, again those spines in the axles, that time I caught it flowering and have more details!

Psychotria racemosa does look right!

http://biogeodb.stri.si.edu/bo...

Metrosideros said:Psychotria racemosa does look right!

http://biogeodb.stri.si.edu/bo...

That makes three of us, I think you can call this one solved Myriam.

http://www.discoverlife.org/mp...

Dave and Janet!