Customize interface for elder / older users
You don't need a phone specifically geared to "elderly people", as you will likely just end up paying more for less just to get that tag.

The latest Android N (Nougat) version offers a quite advanced Screen Zoom function that can enlarge all screen items. You can see it in action here.

On older Android versions, you mostly have the option of setting text size, and if you have root or install a custom ROM like Cyanogenmod (which in its official versions is usually totally unproblematic for daily use even by non-tech-savvy users), you can change the device's DPI setting, which basically lets the system know about the physical screen size of the phone. 

By setting the DPI value higher, the system believes your screen is smaller than in reality and makes both text size and icons larger (in a limited number of increments, not continuously). I have found in the past that this works quite well (using it for instance to enlarge all items, including map scale, in navigation apps).

So I would recommend choosing a well-reviewed large-screen phone (the largest your father-in-law cares to pocket) with Android N software (or with Cyanogenmod support) and enlarging the screen items as detailed above.