I recommend getting UniKey and setting up the VNI keyboard on your computer. It toggles easily and I think it is the best of the vietnamese keyboard setups out there.
That means there will be a lot of on-screen keys for each. I do hope Duolingo will come up with something. I have no control over this.
I have a really basic Android tablet that lets me install a Vietnamese keyboard. It looks like an English one, but when i hold a key down that has options, e.g. vowels, it pops up all the different choices for that key, eg when I hold d I get đ as a choice, but when I hold a, I get 17 to choose from. It works well and maybe Duolingo will have to look at something similar.
I have found this useful. I click between the websites, writing the answer here and then copying it into duolingo with the usual copy and paste keyboard shortcuts. http://usefulwebtool.com/en/vietnamese-keyboard.php