Allowing the tomatoes to ripen gradually as above will work, and give him ripe tomatoes for many months into winter. Keep an eye on them, and pull them out for special attention when they begin to colour. If he needs them to hurry up, he can store a few at a time with apples.
Also, prepping and freezing them works. Scalding, peeling, chopping, cooking, then freezing them (or leaving the cooking until after it's thawed), as a mixed ratatouille with other chopped vegetables and fruit (e.g. squash, zucchini, pumpkin, potato, apple, beans, peas, eggplant, peppers) is tasty, and the ingredients only have to stay somewhat separate - not totally so.
You can even make sweet or savoury pie filling with apples and chopped green tomatoes, and sweetener, herbs and spices as appropriate. Or pizza topping. Or soup - even green tomato gazpacho.
Green tomato jam.
Pickled green tomatoes.
Green tomato pickles (different), green tomato piccalilli or chow-chow, green tomato relish, and green tomato chutney.
There's a lot of overlap, but each one will get you some unique recipes.
You can, of course, make hot or savoury tomato sauce with vinegar and/or sugar - red with red tomatoes and peppers, green with green tomatoes and peppers, or yellow with mustard (and maybe turmeric), tomatoes and peppers. Heck, if you wanted to go crazy you could make it blue with blueberries and grape or blackcurrant juice, and maybe "red" cabbage for a pickle. It looks distinctly odd or off, but it tastes fine, and kids often love it.