Thank you for your reply vgkg, I hadn't considered insects as a potential culprit but you may be onto something! 

I don't know if it's flea beetles though. Yes we do have them in Malta, BUT apparently papaya leaf extract is actually a very effecient flea beetle deterrent! So it would be unlikely they would go for papaya. 

https://www.researchgate.net/publication/262804117_Evaluation_of_Botanical_Insecticides_against_flea_beetles_Podagrica_sjostedti_and_Podagrica_uniforma_on_okra

I should note also that, whatever is causing the damage, it has completely spared the rose and the cherry tomato plants that are right next to the papaya.

Ime flea beetles make holes right through the leaf, not surface blemishes. Those marks look more fungal to me, possibly brought on by physical damage from the weather and the fact that, even in Malta, December could get a bit chilly for Papaya.

Thank you floral_uk!

We are having a very warm winter down here so far, it's still 22°C in the daytime and about 15° at night, although the temps should start to drop a little next week.

The papayas are near a south facing wall, in a courtyard sheltered from any strong winds. They should be able to handle the Maltese winter as we are well within their hardiness zone, although their growth will probably be slower in the next couple months.

I'm afraid you may be right and it could be fungus after all.

I will try some neem oil spray, hopefully that might help.

I know nothing about papaya but would like to ask a question.

Aren't those little 3" pots getting too small for the plants?

Hi @BillMN-z-2-2-4!

There are six seedlings, they sprouted in late July. The four strongest ones were potted up last month into 3 gallon pots. The two less strong ones are still in 1 gallon pots, I will pot them up this weekend. There were more, but they were weak so I threw them out. 

The smaller pots you see in the pic are the one gallon pots. Unfortunately, all of them are affected by the spotting, even those in the 3 gallon pots.

Papayas aren't self-fertile, so you have to keep a bunch of seedlings for a while until they bloom, then you can tell which ones are male/female.

They are all getting potted up again in January to five gallon pots. Once I figure out the males/females, I will keep only three (one male two females, if possible) and put them in much larger pots.

That is, if whatever is causing the spots doesn't kill them beforehand!

Thank you. That's very interesting to hear about these more exotic trees (that we don't have here). :-)