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Something like http://www.telstra.com.au/mobile-phones/mobile-phones/telstr...?

(There was one with larger buttons, but I can't find it)

While this might not be the exact answer you were looking for, but people can buy a cheap android phone and put this launcher.

https://play.google.com/store/apps/details?id=name.kunes.and...

iNO Mobile here in Singapore has a whole series of elderly-targeted phones, here's one:

http://www.inomobile.com.sg/2012/07/ino-cp10/

actual retail price now is SGD 79, which is about USD 65. I'm not sure if I can get these at our 7-Elevens, but I think they have something similar with large keys.

They lamented that they could not find a phone for my elderly grandmother

Check out Doro (www.doro.com/). Quoting from the top of their website:

"Doro is a Swedish company developing telecom products specially adapted to the growing worldwide population of seniors."