Well I did grow a papaya from seed this year but when I put it outside it burned in the sun and never looked the same :( Maybe Ill try again next year, but I think it can be done. You can always plant them in the ground and dig them up and pot them during the winter. You might not get mature fruit, but you will definitely get compliments on it not to mention a pretty quick growing tropical!!!
Good luck!
-Alex

I am in the process of doing so. I bought one at the grocery store and germinated a bunch of seeds. I presently have around 12 seedlings with the biggest ones being around 6 inches or so. I will bring them in come fall and hopefully continue the process next spring.

They are easy to germinate. Heed Alex's warning. They must be eased into full sun or they get torched and turn yellow. And you must be careful when repotting as they have an extensive root system, even when young. Otherwise, they seem akin to growing bananas.

There is a Hawaiian species that tops out at 6 feet or so. They might be easier than these that grow 20 feet.

Thanks Alex and Jack. I grew a payaya years ago, but it ended up dying. I don't think they like cold feet, and it just kind of died inside during the winter. Maybe I should cut back on watering it in winter. I've learned to use a soil moisture meter only the last couple of years, and what a difference it makes! All of my potted plants have done a lot better by watering them according to the actual moisture content in the soil, instead of just guessing!

Papayas are not really difficult to overwinter. I would suggest you try to get a dwarf papaya as it's obviously easier to bring into the house in the Fall. Really cut down on watering in the Winter. It may loose a bunch of leaves but the center ones will remain green.

My papaya was doing its best indoors. I think you should try to germinate it outside so that way it might be used to the higher light levels. I germinated mine indoors and it really couldnt handle anything at all.
In the winter give it a sunny spot and not too much water and it should be fine! I definitely think Im going to try them again but the summers almost gone so the time to sow them outside is definitely now if you want them to be germinated for the winter. From my experience they take about a week to germinate and a month to pass the fragile seedling stage.
Good luck! Hopefully they do better this time around for the both of us!
-Alex