If they don't have a computer, they probably don't have the internet connection they'll also need for your described work flow. In the end, the internet connection is going to cost more than the computer, even with your $170 option.
Of course, they could go use internet at the library, but then it needs to be portable (higher cost) and they already had an option to use a computer there so what are we actually solving.
I think trying to get below the price point of a raspberry pi isn't going to be worth the trouble. I think you can lower your price point on that if you try though.. Looking to price on up cheaply I get: pi 2b ($35), case ($4), wifi ($4), micro sdhc ($4), ac usb charger ($3), usb wire ($2), keyboard ($7), mouse ($2). ...for a grand total of: $61 dollars... OK, and I went with the cheapest available (mostly) so a prudent choice would likely cost a few dollars more.. That means that basically your estimate was right on! Doh! I guess I take for granted that I have almost all those cheap little parts already laying all over the place at our house..
Still, I think you can help them put the parts together, and it's probably your best bet.. Anything cheaper is going to quickly lose functionality/quality. A Pi is a really solid little machine for basic computing, and it's really well supported.