Seeing as the departure is not until late January, it leaves them plenty of time to acquire a turist visa from the nearest Thai embassy. That would both be the cheapest option (while avoiding overstay), and they would not have to spend potentially a whole day of the holiday in an immigration office to extend their 30 day visa exempt.
you could get a multi entry turist visa before going to Thailand. That would get you almost 9 months of stay in total, after which you could go to a nearby country and get another single entry visa for 60 days and extend another 30.. Or you could get either the single or multi entry before coming to Thailand, and then before that expires, apply for a one year extension at immigration based on being the guardian of your son. I believe that would require 500.000 baht in a thai bank in your name, I dont recall how long it has to be seasoned, but i am sure others here can tell you that.